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7 does not divide a + b if 7 divides a^2 + b^2 + 1

Source: 2018 SMT - Stanford Math Tournament , Team Round, Proof Question 1

January 26, 2022
number theorydividesdivisible

Problem Statement

Prove that if 77 divides a2+b2+1a^2 + b^2 + 1, then 77 does not divide a+ba + b.
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