 If formula_48 is an odd prime, this is equal to the Legendre symbol, and decides whether formula_25 is a quadratic residue modulo formula_48.On the other hand, since the equivalence of formula_51 to the Jacobi symbol holds for all odd primes, but not necessarily for composite numbers, calculating both and comparing them can be used as a primality test, specifically the Solovay-Strassen primality test.Composite numbers for which the congruence holds for a given formula_25 are called Euler–Jacobi pseudoprimes to base formula_25.