MathDB
Q 4

Source:

May 25, 2007
algebrapolynomialinequalitiescomplex analysiscomplex numbersPolynomials

Problem Statement

A prime pp has decimal digits pnpn−1⋯p0p_{n}p_{n-1} \cdots p_0 with pn>1p_{n}>1. Show that the polynomial pnxn+pn−1xn−1+⋯+p1x+p0p_{n}x^{n} + p_{n-1}x^{n-1}+\cdots+ p_{1}x + p_0 cannot be represented as a product of two nonconstant polynomials with integer coefficients
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