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2005 OIM Problems/Problem 4

Revision as of 17:17, 14 December 2023 by Tomasdiaz (talk | contribs) (Created page with "== Problem == Given two positive integers <math>a</math> and <math>b</math>, <math>a\nabla b</math> denotes the remainder obtained by dividing <math>a</math> by <math>b</math>...")
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Problem

Given two positive integers $a$ and $b$, $a\nabla b$ denotes the remainder obtained by dividing $a$ by $b$. This remainder is one of the numbers $0, 1, \cdots , b - 1$. Find all the pairs of numbers $(a, p)$ such that $p$ is prime and it holds that

\[(a\nabla p)+(a\nabla 2p)+(a\nabla 3p)+(a\nabla 4p)=a+p\]

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

Solution

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See also

OIM Problems and Solutions

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