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2-parameter diophantine system (HOMC 2017 S Q6)

Source:

September 8, 2019
Diophantine Equationsdiophantinesystem of equationsnumber theoryparametric equation

Problem Statement

Find all pairs of integers a,ba, b such that the following system of equations has a unique integral solution (x,y,z)(x , y , z ) : {x+y=a−1x(y+1)−z2=b\begin{cases}x + y = a - 1 \\ x(y + 1) - z^2 = b \end{cases}
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