Math Olympiad | A Nice Algebra Problem | Integer Solutions...

This equation represents a classic problem of solving for two variables in mathematics. Known as the difference of squares, this equation frequently appears in math Olympiads, challenging students to use factorization and number theory to find integer solutions for and .

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[walterwen]

Math Olympiad: x² – y² = 13; x, y = ?
x² > y² > 13; x² – y² = (1)(13) = (7 – 6)(7 + 6) = (± 7)² – (± 6)² = (± 6i)² – (± 7i)²
x = 7, y = 6; x = – 7, y = – 6; x = 6i, y = 7i; x = 6i, y = – 7i;
x = – 6i, y = 7i; x = – 6i, y = – 7i;
Answer check:
x² – y² = 13; Confirmed as shown
Final answer:
x = 7, y = 6; x = 7, y = – 6; x = – 7, y = 6; x = – 7, y = – 6
4 sets of imaginary value roots, if acceptable;
x = 6i, y = 7i; x = 6i, y = – 7i; x = – 6i, y = 7i or x = – 6i, y = – 7i