Compute 17^7121 (mod 11).

In the expansion of (4x -2/x)8 or (4x -2x^-1)8, find the following: a)the term containing x^6 b)the constant term (the term that does not contain x) I know a) is -262144x^6 and -4096/x^6 and b) is 286720 but i don't know how to do the formula of Tk+1 = C (n,k) a ^n-k x k

Solve 2^x ≡ 79 mod 101 when given 5^11 ≡ 79 mod 101.

According to Fermat’s Little Theorem, which of the following is an inverse of 2 (mod 83)?   1.  2^802.  2^84 3.  2^81 4.  2^83 5.  2^82

Use Fermat’s little theorem to find the least residue of 863 modulo 31.

Find the inverse of 79 mod 191 using the Extended Euclidean Algorithm

Let a be a natural number such that gcd(a, 10) = 1. Use Euler’s theorem to prove that a^40n+1 and a must have the same ones and tens digits in their base ten expansions

4) Find 25725 (mod 31)

Combine Fermat’s Little Theorem with the Chinese Remainder Theorem to calculate the least residue of 3^1453 modulo 35.

use the "successive squaring" method to check 'by hand and modest calculator' that a^48610 == 1 (mod 48611), as in the Fermat Primality Test, for a = 2, 31, and 257.