MathDB

4

Part of 2014 IMAC Arhimede

Problems(1)

P(x), P(x^2) are rational then x is rational, where P(t)=1+t +t^2 +...++ t^{2n}

Source: IMAC Arhimede 2014 p4

5/6/2019
Let nn be a natural number and let P(t)=1+t+t2+...+t2nP (t) = 1 + t + t^2 + ... + t^{2n}. If xāˆˆRx \in R such that P(x)P (x) and P(x2)P (x^2) are rational numbers, prove that xx is rational number.
polynomialalgebraSum of powersSumrational