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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1999-05-25