2005 OIM Problems/Problem 4
Problem
Given two positive integers 
and 
, 
denotes the remainder obtained by dividing by . This remainder is one of the numbers 
. Find all the pairs of numbers 
such that 
is prime and it holds that
![\[(a\nabla p)+(a\nabla 2p)+(a\nabla 3p)+(a\nabla 4p)=a+p\]](http://latex.artofproblemsolving.com/4/b/4/4b49455bcd3937013c5d0c578cd3d07fa8a861dd.png)
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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