Fermat Quotients for Composite Moduli Original Research Article

Analogues of Fermat quotients for a composite modulusmgreater-or-equal, slanted2 are investigated, with special emphasis on various congruences. In particular, the numbersmfor whichaφ(m)≡1 (mod m2), where gcd(a, m)=1, (“Wieferich numbers with basea”) are completely characterized in terms of the Wieferich primes with basea.