IMO 2017 Shortlist A1
Let a1,a2,...,an,k, and M be positive integers su h that a1 a2 ¨¨¨ an “ k and a1a2 ...an “ M. If M ą 1, prove that the p...
Category: Algebra
Problem
Let a1,a2,...,an,k, and M be positive integers su h that
a1
a2 ¨¨¨ an “ k and a1a2 ...an “ M. If M ą 1, prove that the polynomial Ppxq “ Mpx 1qk
´ px a1qpx a2q¨¨¨px ` anq
has no positive roots.
(Trinidad and Tobago)