1) See result (2) here
2) What is that e? by the way What is ?
3) Note that and that by Fermat's Little Theorem: when p is prime (for all integers )
And but we have thus (b)
By (a) and by (b): thus which shows that
If the product of all positive divisors of n is n^2. Prove v(n) [the number of positive divisors function]=4
If n is congruent to k mod 40. Prove e^n is congruent to 2^k mod 55
Prove n^11 is congruent to n mod 33.
Thanks for any help!