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

learn more… | top users | synonyms

12
votes
1answer
1k views

Comparing powers without logarithms

Related to this question and this Project Euler problem (Problem 99), I came up with a recursive algorithm for comparing two numbers of the form $x^y$ (with $x>1$ and $y\ge 0$) without explicit use ...
10
votes
4answers
70k views

Find the sum of all the multiples of 3 or 5 below 1000

How to solve this problem, I can not figure it out: If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23. Find the sum of ...
14
votes
1answer
4k views

How to find the smallest number with just $0$ and $1$ which is divided by a given number?

Every positive integer divide some number whose representation (base $10$) contains only zeroes and ones. One can easily prove that using pigeonhole principle. ...
6
votes
3answers
779 views

Closed form for the sum of even fibonacci numbers?

I recently took a look a project euler, and I am trying to think of a smart way to do number 2. I looked at the sequence, and I saw that the question is basically asking for $$ \sum_{i=1}^n F_{3i} $$ ...
7
votes
4answers
19k views

Find the largest prime factor

I just "solved" the third Project Euler problem: The prime factors of 13195 are 5, 7, 13 and 29. What is the largest prime factor of the number 600851475143 ? With this on Mathematica: <...
4
votes
3answers
961 views

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 ...
9
votes
3answers
32k views

Largest prime factor of 600851475143 [duplicate]

I'm trying to use a program to find the largest prime factor of 600851475143. This is for Project Euler here: http://projecteuler.net/problem=3 I first attempted this with the code that goes through ...
7
votes
3answers
894 views

Project Euler Question 222

Would I be wrong to assume that the solution to this problem: What is the length of the shortest pipe, of internal radius 50mm, that can fully contain 21 balls of radii 30mm, 31mm, ..., 50mm? ......
4
votes
2answers
445 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 $(-1+i)$....
7
votes
3answers
4k views

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 ...
2
votes
0answers
506 views

Counting couples having least common multiple less than a number

Let f(n) be the number of couples (x,y) with x and y positive integers, $x\leq y$ and the least common multiple of x and y equal to n. Let g be the summatory function of f, i.e.: $g(n) = \sum_{i=1}...
2
votes
2answers
407 views

Longest antichain of divisors

I Need to find a way to calculate the length of the longest antichain of divisors of a number N (example 720 - 6, or 1450 - 4), with divisibility as operation. Is there a universally applicable way to ...
1
vote
1answer
754 views

Project Euler $420$ [closed]

So the question is: We define $F(N)$ as the number of the $2\times 2$ positive integer matrices which have a trace less than $N$ and which can be expressed as a square of a positive integer matrix ...
1
vote
1answer
2k views

How to find large prime factors without using computer?

What is the largest prime factor of the number 600851475143 ? This is the third problem of Project Euler. How to approach this mathematically (without computer programming) ?
5
votes
2answers
418 views

Does “triangle” in English exclude degenerate triangles?

Just for fun read few problems on the projeteuler.net website. Number 276 found interesting: Consider the triangles with integer sides a, b and c with a ≤ b ≤ c. An integer sided triangle (a,b,...
2
votes
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 ...