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p(x -2) = x(y -1) , diophantine

Source: 2015 Cuba 2.7

September 20, 2024
number theorydiophantineDiophantine equation

Problem Statement

If pp is a prime number and x,yx, y are positive integers, find in terms of pp, all pairs (x,y)(x, y) that satisfy the equation: p(x−2)=x(y−1).p(x -2) = x(y -1). If x+y=21x+y = 21, find all triples (x,y,p)(x, y, p) that satisfy this equation.
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