If the lattice point

MATHEMATICS · Subjective · AoPS · Mathematics · Follow the Rules · Follow the Rules

Problem

P(x, y, z)

x, y, z > 0

and

x, y, z \in I

with least value of

z

such that the 'P' lies on the planes

7x + 6y + 2z = 272

and

x - y + z = 16

, then the value of

(x + y + z - 42)

is equal to