Inverse of Modulus

Find an inverse of 2 modulo 17.

Solving Congruences

Solve the congruence of 2x ≡ 7 (mod 17)

Solving Systems of Congruences

Find all solutions to the system of congruences: x ≡ 2 (mod 3) x ≡ 1 (mod 4) x ≡ 3 (mod 5)

Fermat's Little Theorem

Use Fermat's Little Theorem to compute 3^302 mod 5, 3^302 mod 7, and 3^302 mod 11. Use your results to find 3 ^ 302 mod 385 (note 385 = 5 . 7 . 11.)

Binary and Hexadecimal Expansions

Show that the binary expansion of a positive integer can be obtained from its hexadecimal expansion by translating each hexadecimal digit into a block of four binary digits.