Problem #PRU-116676

Problems Number Theory Divisibility The greatest common divisor (GCD) and the least common multiplier (LCM). Mutually prime numbers

11–14 4.0

Problem

Rational numbers $x, y, z$ are such that all the numbers $x + y^{2} + z^{2}$ , $x^{2} + y + z^{2}$ , $x^{2} + y^{2} + z$ are integers. Prove that $2 x$ is also an integer.

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