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How many ordered 6-tuples satisfy the system

Source: Vietnam National Mathematical Olympiad 2013, P7, Day 1

January 12, 2013
number theory proposednumber theory

Problem Statement

Find all ordered 6-tuples satisfy following system of modular equation: ab+a′b′≡1ab+a'b' \equiv 1 (mod 15) bc+b′c′≡1bc+b'c' \equiv 1 (mod 15) ca+c′a′≡1ca+c'a' \equiv 1 (mod 15) Given that a,b,c,a′,b′,c′ϵ(0;1;2;...;14)a,b,c,a',b',c' \epsilon (0;1;2;...;14)
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