MathDB

Let

\overline{a_{n}a_{n-1}\ldots a_{1}a_{0}}

be the decimal representation of a prime positive integer such that

n>1

and

a_{n}>1

. Prove that the polynomial

P(x)=a_{n}x^{n}+\ldots +a_{1}x+a_{0}

cannot be written as a product of two non-constant integer polynomials.

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