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p prime iff 1 of a+b-6ab+(p-1)/6 , a+b+6ab+(p-1)/6 \in Z

Source: Czech and Slovak Match 1996 P1

October 1, 2017
primeIntegersnumber theory

Problem Statement

Show that an integer p>3p > 3 is a prime if and only if for every two nonzero integers a,ba,b exactly one of the numbers N1=a+b−6ab+p−16N_1 = a+b-6ab+\frac{p-1}{6} , N2=a+b+6ab+p−16N_2 = a+b+6ab+\frac{p-1}{6} is a nonzero integer.
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