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Solve for x,y,z in integers given p,q are distinct primes

Source: P5: Bosnia and Herzegovina TST 2002

October 7, 2014
number theoryprime numbersalgebra proposedalgebra

Problem Statement

Let pp and qq be different prime numbers. Solve the following system in integers: z+px+z−py=q,z+py−z−px=q.\frac{z+ p}x+\frac{z-p}y= q,\\ \frac{z+ p}y -\frac{z-p}x= q.
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