aⁿ≡c (mod n)
(F10 Residues of powers of two)

Graham asked about the residue of 2ⁿ mod n.
Lehmer found the smallest solution for 2ⁿ≡3 (mod n),
n=4700063497

I tried to find all the solutions of aⁿ≡c (mod n) where
a : prime under 100, 1 ≤ c ≤ 100, n ≤ 10⁹.

The program is very simple so I just show the results of computation.

The solutions for a=3, c=14, 34, 56 and a=7, c=36 are listed in
The On-Line Encyclopedia of Integer Sequences.

a	c : no solution under 1010
2	69
3	14, 34, 56, 74
5	58
7	36, 66, 86
11	52, 94
13	36, 54, 59, 80, 92
17	16, 30, 64, 100
19	62, 78, 86
23	42, 64, 84
29	18
31	24, 54, 98
37
41	42
43
47	36, 46, 64, 90
53	54, 64, 84, 96
59	36, 42
61	32, 78
67	50
71	88
73	78
79
83	54
89	82
97	50