# 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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### Bell-like recurrence

Let $$A(n)=\sum_{k=0}^{n-1}\binom{n}{k}A(k)+n!,\quad A(0)=1$$ $$B(n)=\sum_{k=0}^{n-1}\binom{n}{k}B(k)-n!-n!\sum_{k=1}^{n}\frac{1}{k!},\quad B(0)=-1.$$ I'm interested in computing $S(n)=A(n)+B(n)$ ...
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### 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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### 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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### Magic Square Combinatorics

This question has been noted to be close to a Project Euler question. Please Help me with this question:Considering a 4*4 magic square ,How many ways are there to fill each square with an integer ...
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### Number of closed paths formed by arcs of one fifth of a circle

**I was trying to solve the following issue: Find the number of possible closed paths using one fifth of an arc ($72^o$), where at each time step we can move either clockwise or anti-clockwise. in ...
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### 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\...