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

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12
votes
1answer
443 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 ...
5
votes
3answers
246 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 $$ \sum_{i=1}^n F_{3i} $$ ...
6
votes
3answers
8k 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: ...
2
votes
3answers
132 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 ...
2
votes
3answers
8k 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 ...
2
votes
0answers
425 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) = ...
1
vote
4answers
13k 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 ...
4
votes
2answers
223 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 ...
1
vote
1answer
777 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) ?