Haupt-Exponent
The smallest exponent 
for which 
, where 
and 
are given numbers, is the haupt-exponent of (mod). The number of bases having a haupt-exponent is 
, where is the Totient Function. Cunningham(1922) published the haupt-exponents for primes to 25409 and bases 2, 3, 5, 6, 7, 10, 11, and 12.
References
Cunningham, A. Haupt-Exponents, Residue Indices, Primitive Roots. London: F. Hodgson, 1922.
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