How many different triples of numbers satisfy the equation

MATHEMATICS · Subjective · AoPS · Mathematics · Follow the Rules · Follow the Rules

Problem

How many different triples of numbers (a,b,c)(a, b, c) satisfy the equation a2+bc=b2+aca^2 + bc = b^2 + ac, if aa, bb, and cc are integers from 1 to 5, inclusive? (The numbers aa, bb, and cc are not necessarily different.)

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