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Indian TST Algebra

Source: Selection Test 2

June 20, 2011
calculusintegrationalgebra unsolvedalgebra

Problem Statement

Suppose a1,…,ana_1,\ldots,a_n are non-integral real numbers for n≥2n\geq 2 such that a1k+…+ank{a_1}^k+\ldots+{a_n}^k is an integer for all integers 1≤k≤n1\leq k\leq n. Prove that none of a1,…,ana_1,\ldots,a_n is rational.
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