TR-MO-R1 2010 Problem 26

$m$ nin aşağıdaki değerlerinden hangisi için $3x^2+4y^2-5z^2 = m$ eşitliğini sağlayan $(x, y, z)$ pozitif tam sayı üçlüsü yoktur?

a) 16 b) 14 c) 12 d) 10 e) 8

Official text Turkish Mathematical Olympiad, first round 2010 official paper, page 8. Quoted with source.

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