JBMO-SL 2009 A1

Determine all integers $a, b, c$ satisfying the identities:

$\begin{gathered} a+b+c=15 \\ (a-3)^{3}+(b-5)^{3}+(c-7)^{3}=540 \end{gathered}$

Dataset text NuminaMath olympiads. Quoted with source.

Show the answer

(a-3)(b-5)(c-7)=180

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.