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TOT 478 1995 Autumn S A2 n irrationals if their product -x_= odd integer

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July 9, 2024
irrational numbernumber theoryalgebra

Problem Statement

Let pp be the product of nn real numbers x1x_1, x2x_2,......, xnx_n. Prove that if p−xkp - x_k is an odd integer for k=1,2,...,nk = 1, 2,..., n, then each of the numbers x1x_1, x2x_2,......, xnx_nis irrational.
(G Galperin)
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