4
votes
0answers
47 views

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 ...
0
votes
3answers
77 views

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 ...
2
votes
1answer
52 views

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!
2
votes
0answers
81 views

Need to find a better algorithm to solve a project euler problem dealing with coprime pairs.

I've been working on this for a while and found several solutions so far, but none are fast enough to find the necessary $S(10^7)$. Here is the question: For an integer $M$, we define $R(M)$ as ...
0
votes
1answer
87 views

Non-Recursive Fundamental Recurrence Formulas

Is there a non-recursive version of the fundamental recurrence formulas for continued fractions? I am trying to compute $A_{1000}$, and it is taking me an extremely long time. By the way, I am ...
1
vote
3answers
1k views

Find smallest multiple of specific set of numbers

I was trying to solve the 5th problem on project-euler.net, wich is finding the smallest number wich was multiple of each number in a specific set, in this case, $[1 ... 20]$. First I thought of was ...
0
votes
5answers
532 views

Every odd composite $=$ prime ${}+ 2x^2$

I was looking through some project-euler questions and I came across one that said Every odd composite number can be written as the sum of a prime and twice a square...This was proven false. ...
9
votes
0answers
612 views

How many integer solutions to a diophantine equation

Starting with the equation: $\frac{1}{a}+\frac{1}{b}=\frac{p}{10^n}$, I reached the equation: $10^{n-log(p)} = \frac{ab}{a+b}$. Now given the positive integer $n$, for what integer values of $p$ ...
4
votes
2answers
215 views

Solving $\phi (n) < (n-1) \cdot \frac{15499}{94744} $

I am working on challenge 243 from Project Euler (PE 243). The question is: $$\text{Solve } \phi (n) < (n-1)\cdot \frac{15499}{94744}$$ I can calculate $\phi(n)$ for any $n$, but I think the $n$ ...
1
vote
1answer
272 views

Algorithm for generating an ordered list of pair products

For problem 4 in the euler project part of the assignment is to generate a list of products of 3-digit numbers. The easy way is to just do a cartesian product (I think it's called), and after that ...
2
votes
3answers
2k views

Generating Numeric Palindromes.

I have just started the Euler project, and felt like I didn't get the fourth problem right...I used string conversion to test if my numbers were symmetrical, instead of relying on (the much faster) ...
2
votes
2answers
1k views

Computing Non-zero End Digits of Large Factorials

Any large factorial will have a number of zero behind it, and one could write an expression to compute the number of trailing zeros, but how would one go about computing the non-zero end digits? E.g. ...
35
votes
7answers
3k views

Project Euler, Problem #25

Problem #25 from Project Euler asks: What is the first term in the Fibonacci sequence to contain 1000 digits? The brute force way of solving this is by simply telling the computer to generate ...