12

Part of 1992 Poland - First Round

Problems(1)

Factoring x^n+4

Source: Poland Math Olympiad 1992 Round 1 #12

Prove that the polynomial

x^n+4

can be expressed as a product of two polynomials (each with degree less than

n

) with integer coefficients, if and only if

n

is divisible by

4

algebrapolynomial