Number theory · Diophantine equations · Quadratic residues · Parity · Infinite descent
Find all solutions of the equation
\[ 6\left(6a^{2} + 3b^{2} + c^{2}\right) = 5d^{2} \]
in integers \(a\), \(b\), \(c\), \(d\).
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Serbian Municipal Competition 2014, high school grade I, category A, problem 3. Organized by the Mathematical Society of Serbia (DMS). Source