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existence given P(1/n)=f(n)

Source: VJIMC 2011 1.1

June 1, 2021

Polynomialsnumber theory

Problem Statement

(a) Is there a polynomial

P(x)

with real coefficients such that

P\left(\frac1k\right)=\frac{k+2}k

for all positive integers

k

? (b) Is there a polynomial

P(x)

with real coefficients such that

P\left(\frac1k\right)=\frac1{2k+1}

for all positive integers

k

?

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