 Over GF(2), is a primitive polynomial and all other primitive polynomials have an odd number of terms, since any polynomial mod 2 with an even number of terms is divisible by (it has 1 as a root).An irreducible polynomial "F"("x") of degree "m" over GF("p"), where "p" is prime, is a primitive polynomial if the smallest positive integer "n" such that "F"("x") divides is .Over GF("p""m") there are exactly primitive polynomials of degree "m", where "φ" is Euler's totient function.