A prime p is called a Wieferich prime in base a > 1, if (a, p) = 1 and ap1 1 (mod p2). An integer m > 1 is called a Wieferich number in base a > 1, if (a, m) = 1 and a'(m) 1 (mod m2), where ' is the Euler function. In 2007, Banks, Luca, and Shparlinski proved that if the set of Wieferich primes in base 2 is finite, then the set of Wieferich numbers in base 2 is also finite. Moreover, they found an upper bound for the largest element of this set. Here we present a procedure in which the largest element can be constructed in any base.
展开▼
