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solve in N: p(x-2)=x(y-1) and x+y=21 , where p is prime

Source: Greece JBMO TST 2013 p3

April 29, 2019
number theoryprimeDiophantine equationDiophantine Equations

Problem Statement

If pp is a prime positive integer and x,yx,y are positive integers, find , in terms of pp, all pairs (x,y)(x,y) that are solutions of the equation: p(x−2)=x(y−1)p(x-2)=x(y-1). (1) If it is also given that x+y=21x+y=21, find all triplets (x,y,p)(x,y,p) that are solutions to equation (1).
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