MathDB

Putnam 2007 B4

Source:

December 3, 2007

Putnamalgebrapolynomialcollege contests

Problem Statement

Let

n

be a positive integer. Find the number of pairs

P,Q

of polynomials with real coefficients such that (P(X))^2\plus{}(Q(X))^2\equal{}X^{2n}\plus{}1 and

\text{deg}P<\text{deg}{Q}.