We give sufficient cohomological criteria for the classes of given varieties over a field k to be algebraically independent in the Grothendieck ring of varieties over k and construct some examples. m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m K p−1 Q Observe that by construction gcd(n, N ) = 1 (N is a product of primes different from the prime n) and hence gcd(p n − 1, p N − 1) = p − 1 which implies as recalled