Wolfram Demonstrations Project

Congruences of the form

display many regular patterns, as explained by theorems from Fermat and Euler, among others. The plot shows the values of

within the complete residue system

for domain values

, the modulus

, and the exponent

Snapshot 1: little Fermat theorem

Snapshot 2: quadratic residues of 7

The initial settings are a particular demonstration of Euler's criterion.

Contributed by: Richard Roe

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Exponential Congruences