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Sum x^k/k! + 1 = 0 has no rational roots

Source: IMO Shortlist 1989, Problem 4, ILL 7

September 18, 2008
algebraequationpolynomialDiophantine equationRational rootsIMO Shortlist

Problem Statement

Prove that ∀n>1,n∈N \forall n > 1, n \in \mathbb{N} the equation \sum^n_{k\equal{}1} \frac{x^k}{k!} \plus{} 1 \equal{} 0 has no rational roots.
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