# Tagged Questions

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

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### 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 ...
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### 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 ...
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### 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. ...
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### 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 $$\sum_{i=1}^n F_{3i}$$ ...
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### 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: <...
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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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### 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 ...
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### 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? ......
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### 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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### 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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### 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) ?