MathDB

Determine all polynomials with integral coefficients

P(x)

such that if

a,b,c

are the sides of a right-angled triangle, then

P(a), P(b), P(c)

are also the sides of a right-angled triangle. (Sides of a triangle are necessarily positive. Note that it's not necessary for the order of sides to be preserved; if

c

is the hypotenuse of the first triangle, it's not necessary that

P(c)

is the hypotenuse of the second triangle, and similar with the others.)

Problem Statement