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Prove that the equation has $x^2-x+3-ps=0$ with $x,s\in\mathbb{Z}$ has solutions

Source: Moldova TST 1995

August 8, 2023

number theoryprime numbers

Problem Statement

Let

p{}

be a prime number. Prove that the equation has

x^2-x+3-ps=0

with

x,s\in\mathbb{Z}

has solutions if and only if the equation

y^2-y+25-pt=0

with

y,t\in\mathbb{Z}

has solutions.