Problem #PRU-109787

Problems Algebra Polynomials Algebraic identities for polynomials Factoring polynomials Calculus Real numbers Rational and irrational numbers

14–16 4.0

Problem

A numeric set $M$ containing 2003 distinct numbers is such that for every two distinct elements $a, b$ in $M$ , the number $a^{2} + b \sqrt{2}$ is rational. Prove that for any $a$ in $M$ the number $q \sqrt{2}$ is rational.

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