Prove that every nonzero coefficient of the Taylor series of (1-x+x²) ex about x = 0 is a rational number whose numerator (in lowest terms) is either 1 or a prime number. Let Pn(x) = 1 + 2x+3x²+ +nan-1. Prove that the polynomials P; (x) and P₁(x) are relatively prime for all positive integers j and k with j ‡ k.

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