Project Euler is a series of challenging mathematical/computer programming problems. Please see the site and rules before posting.

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Project Euler's, Problem #565

Project Euler's, Problem #565 states: Let $\sigma(n)$ be the sum of the divisors of $n$. E.g. the divisors of $4$ are $1, 2$ and $4$, so $\sigma(4)=7$. The numbers $n$ not exceeding $20$ ...
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1answer
65 views

How many sets correspond to connected graphs

I'm trying to solve this project euler problem. I don't want to get too much help, since that would defeat the purpose, but I'm hitting a wall, so I'm asking a related problem here, from which I'll ...
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2answers
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Possible mis-interpretation in Project Euler #21

Here is the problem statement for Problem 21 of Project Euler. Let $d(n)$ be defined as the sum of proper divisors of $n$ (numbers less than $n$ which divide evenly into $n$). If $d(a) = b$ ...
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The largest product of two n-digit numbers which is palindrome

Project Euler: 4 is stated as follows: Largest palindrome product A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 ...
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Game of Nim: Losing Positions [closed]

If you have heard of the game Nim, this is a version of the game. However, in this version, the players can only remove the amount of stones from the pile which is coprime to the current pile size. ...
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1answer
81 views

Project Euler 106: Necessary and sufficient conditions

Problem Statement Let S(A) represent the sum of elements in set A of size n. We shall call it a special sum set if for any two non-empty disjoint subsets, B and C, the following properties are ...
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1answer
86 views

Help Project Euler Problem 269

I am stuck on prob 269 Project Euler. I've just tried brute force method to attempt this problem the example provided by PE For example, $P_{5703}(x)$ = $5x^3 + 7x^2 + 3$. We can see that: P$_n(0)$...
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2answers
80 views

Proof that nonconstant polynomial cannot have the same value at all integer points

I am reading the solution to the Project Euler problem 28 here, specifically the one under 'Deriving a non-iterative formula'. That solution first deduces the degree of the polynomial, and then ...
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2answers
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(Soft Question) Is it bad to use Sage built in functions instead of creating my own?

I've been doing Project-Euler just as a way to increase my competency in computer science. I'm currently a Pure and Applied Math major who recently adopted computer science as a minor in order to ...
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0answers
64 views

How to simplify a sum of complex divisors?

This question arises from Project Euler 153. That problem asks for the sum of all complex divisors of all natural numbers up to a maximum, where a complex divisor is a complex number of the form a + ...
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160 views

Solving Cardano Triplets

Reading https://projecteuler.net/problem=251 I'm attempting to solve the example provided : $ 3 \sqrt {a + b \sqrt c} $ + $ 3 \sqrt {a - b \sqrt c} $ = 1 a=2 b=1 c=5 $ 3\sqrt {2+(1)\sqrt5} + 3\...
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610 views

Project Euler, Problem #529 10-substrings

Have anyone tried the problem 529? I tried but I'm confronted to a very high complexity $O(N^2)$ with $N$ being the length of the number. The code is: ...
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2answers
276 views

Expected value of a guessing game

I'm trying to solve project euler 527, I don't understand how the expected value of B(6) is taken. A secret integer t is selected at random within the range 1 ≤ t ≤ n. The goal is to guess ...
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2answers
106 views

Explaining solution of Project Euler problem #5

Here is the problem. Pretty simple to brute force, but more gently solutions are not that easy to understand, and I'm not talking about programming issue, but math-affiliated. For example, I'm ...
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86 views

About an answer given for Project Euler 19

The problem is here and someone gave this answer but I don't understand it even if I know the rule of large numbers. If you want to write a code for this, it is really boring. On the other hand, ...
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186 views

Project Euler Problem #87 - Prime power triples

I found this problem in Project Euler: https://projecteuler.net/problem=87 The smallest number expressible as the sum of a prime square, prime cube, and prime fourth power is $28$. In fact, ...
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1answer
72 views

Finding the last nonzero digit of the factorial of a large number

This problem is from projecteuler problem 160. I am not looking for an answer or anything like that I just got stuck on some of the mathematics and am looking for some help. Instead of solving the ...
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221 views

Calculating two rotation angles from xyz coordinates for dummies

This post is a bit verbose so that others who come later may benefit from my thick headedness. I am attempting to construct a primitives composition and constructed solids geometry parser/processor ...
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1answer
99 views

Summation of a function

Let $n$ is a positive integer. $n = p_1^{e_1}p_2^{e_2}...p_k^{e_k}$ is the complete prime factorization of $n$. Let me define a function $f(n)$ $f(n) = p_1^{c_1}p_2^{c_2}...p_k^{c_k}$ where $c_k = ...
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2answers
315 views

square of digits - why does it always contain 1 or 89 [closed]

I attempted project euler problem 92, while I passed it, my solution works, but had just...awful performance. So I would like to try again tomorrow. In the meantime understanding why the iteration ...
0
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1answer
110 views

Where is my formula false??

I wrote a formula that returned how many numbers in a given row of pascals triangle are divisible by a given prime. This formula was created to answer https://projecteuler.net/problem=148. I was ...
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1answer
105 views

Number of 1s in after converting number to base -1+i

Regarding to Base conversion: How to convert between Decimal and a Complex base? Let $s(a,b)$ is a number of $1$ after converting complex number $a+bi$ to base $-1+i$. It's easy to implement that ...
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453 views

Base conversion: How to convert between Decimal and a Complex base?

My motivation for this question is exploring beyond the ideas in Project Euler Problem 508. In that problem, it is helpful to know how to convert between a decimal number and a number in base $(-1+i)$....
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1answer
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Addition chain search tree pruning by discarding non-minimal chains

An addition chain is an ordered tuple of numbers, starting with $1$, such that each number after $1$ can be expressed as the sum of two smaller numbers in the chain. An example of an addition chain ...
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1answer
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How to find $a_n$ series from Dirichlet generating function

I am solving problems from Project Euler. Solutions for some of the problems is $n^{\rm th}$ term of a series. I know Dirichlet generating functions. How to find $n^{\rm th}$ term of a series from ...
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2answers
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Cubes differences and primality

In an exercise (Project Euler 131, not to mention it), we are looking for perfect cubes of the form $n^3 + n^2 p$, where p is prime. I finally got the answer by trial and error but I don't understand ...
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Finding prime factors by taking the square root

I'm trying to solve the third Project Euler problem and I'd like a little help understanding a mathematical concept underlying my tentative solution. The question reads: The prime factors of ...
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1answer
373 views

Find the sum of all the multiples of 3 or 5 below 1000 (Break down)

I know that this has been posted before but I can't grasp how it actually works. I'm a 16 year old in the 10th grade and am interested in algorithms. I've looked in multiple places on the web but am ...
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49 views

How to compute a slowly converging series to 10 decimals places of accuracy?

I'm looking at a Project Euler problem, where a harmonic series is modified such that it excludes terms where a digit appears three times consecutively in the denominator. So this series would exclude ...
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1answer
110 views

Largest prime factor of a number

In Project Euler problem 3, where we have to find the largest prime factor of a number, one of the solution i came across is ...
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3answers
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Are there any mathematics “problem websites” similar to Project Euler?

Are there any mathematics websites similar to Projet Euler, a website which hosts math-heavy programming questions, many of which can be solved with a pen and paper? I've become almost addicted to ...
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Computing question: A quadratic which gives primes [closed]

This is about Project Euler Problem 27. The question is: Considering quadratics of the form $n^2 + an + b$, where $\lvert a \rvert < 1000$ and $\lvert b \rvert < 1000$ Find the product ...
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1answer
385 views

Find the sum of all n, 0 < n < 64,000,000 such that σ2(n) is a perfect square.

I have been working on Project Euler problem 211 for quite some time, and I am stuck. I'm not looking for an answer, I'm simply looking for some guidance. I've written and tested the following code, ...
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4answers
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Sum of $x^x$ final 10 digits

warning/spoiler alert this problem occurs in the euler project. I want to find the last ten digits of the following sum: $$ S = 1^1 + 2^2 + 3^3 + 4^4 + \cdots + 1000^{1000} $$ Finding this ...
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1answer
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Number of paths through a grid

I am attempting to solve Project Euler prob. 204 by hand, and I decided that this method should help a lot. I have the following grid: The numbers indicate the total number of paths from a node at ...
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2answers
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What rules can I apply for divisible numbers?

I'm trying to solve Project Euler problem 12. I've figured out a fast algorithm for the triangle numbers, but to see if they are devisable is just a pain... ...
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1answer
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How does this algorithm find the largest prime factor?

This question on math.stackexchange details an algorithm that can be used to find the largest prime factor of a number. I used it to solve Project Euler #3. Here's a short description of the algorithm:...
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1answer
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Digit Factorial Sum? [duplicate]

This question is founded in Project Euler #34. I originally solved the problem years ago but now I'm moving all the problems over to a new language. As I revisit this problem, I already know the ...
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1answer
122 views

How to find all pairs $(a, b)$ s.t. $(a^2+b^2)/\gcd(a,b) \leq n$ for constant $n$?

Any help is appreciated, this is for my work on http://projecteuler.net/problem=153. Also posted here
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Why does $n^2 \equiv 10 \pmod{30}$ imply $n \equiv 0 \pmod{10}$?

It seems that $n^2 \equiv 10 \pmod{30} \iff n \equiv 0 \pmod{10}$. I found this by calculating $\{n \in \mathbb N_0 \mid n < 30 \land n^2 \equiv 10 \pmod{30}\} = \{10, 20\}$, and noting that 10 ...
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Counting simple quadrilaterals in a rectangular lattice.

I've been trying to make an algorithm to find the number of all possible simple quadrilaterals in a N*M lattice. I already have a brute force solution but since this is a Project Euler problem I ...
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1answer
376 views

Project Euler #453 confusion

So I decided to give a shot on the #453 project euler problem but there is something that confuses me with the numbers given. I decided to start by calculating the possible arrangements of 4 vertices ...
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1answer
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period of recurring decimals

The period of a recurring decimal fraction $1/d$ is equal to the multiplicative order of $10$ mod $d$. For fractions with even period, the digits sum to 9 i.e. $1/7 = 0.(142857)...$ $$142\\ 857\\ \...
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Is there a closed-form or an efficient way to calculate $\sum_{i=1}^{N/2} i(N \mod i) $

I am trying to solve problem 401 of Project Euler, without giving much away, I have broken down the problem into several summations and I am trying to calculate one part, which is: $$ \sum_{i=1}^{N/2}...
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1answer
260 views

How to find positive integers where the multiplicative modular inverse is equal to itself for mod n?

This a question sparked from Project Euler Question. I really devoted so much time to search an efficient solution however no output. What are some possibles theorems or formulas that are useful in ...
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could not able to understand Project Euler 18. “Maximum path sum I”

According to question, By starting at the top of the triangle below and moving to adjacent numbers on the row below, the maximum total from top to bottom is 23. ...
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Project Euler - 34 / Find a mathematical approach for upper bound

145 is a curious number, as 1! + 4! + 5! = 1 + 24 + 120 = 145. Find the sum of all numbers which are equal to the sum of the factorial of their digits. Note: as 1! = 1 and 2! = 2 are not sums they ...
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1answer
613 views

repunit prime factors

So I am working on this problem... which states: A number consisting entirely of ones is called a repunit. We shall define R(k) to be a repunit of length k; for example, R(6) = 111111. Let ...
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1answer
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An Euler problem: How many of these numbers are of the form $a^b$?

How much numbers can be written in the form $a^b$, where $a$ and $b$ are integers that are between $2$ and $100$? How can I start this problem? Any hints please? Thanks!
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1answer
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Heronian isosceles triangles

This is a problem from Project Euler, problem 94. The problem asks about isosceles triangles with integer sides (differing by 1 unit, e.g, 5-5-6) and integer area, which are known to be Heronian ...