A Symmetric Diophantine Constraint

★ 8/10Diophantine Equations number theory algebra Symmetry

Problem

Positive integers $x, y, z$ satisfy

xyz = (14-x)(14-y)(14-z), \qquad x + y + z < 28.

Find the maximum of $x^2 + y^2 + z^2$ .

Answer

Solution

Difficulty	8/10
Topics	Diophantine Equations, number theory, algebra, Symmetry

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