High Quality Content by WIKIPEDIA articles! In number theory, an odd composite integer n is called an Euler–Jacobi pseudoprime to base a, if a and n are coprime, and a(n – 1)/2 = (a/n) (mod n), where (a/n) is the Jacobi symbol. The motivation for this definition is the fact that all prime numbers n satisfy the above equation, as explained in the Legendre symbol article. The equation can be tested rather quickly, which can be used for probabilistic primality testing. These tests are over twice as strong as tests based on Fermat's little theorem.

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