modular arithmetic

The value of 3 51 mod 5 is_________.

The value of the expression $${13^{99}}$$ ($$mod$$ $$17$$), in the range $$0$$ to $$16,$$ is ______________ .

The minimum positive integer p such that (3 p modulo 17) = 1 is

The set $$\left\{ {1,\,\,2,\,\,3,\,\,5,\,\,7,\,\,8,\,\,9} \right\}$$ under multiplication modulo 10 is not a group. Given below are four plausible reasons. Which one of them is fal...

Suppose that two parties A and B wish to setup a common secret key (D - H key) between themselves using the Diffie-Hellman key exchange technique. They agree on 7 as the modulus an...

What is the minimum number of ordered pairs of non-negative numbers that should be chosen to ensure that there are two pairs $$(a, b)$$ and $$(c, d)$$ in the chosen set such that $...

The set $$\left\{ {1,\,\,2,\,\,4,\,\,7,\,\,8,\,\,11,\,\,13,\,\,14} \right\}$$ is a group under multiplication modulo $$15$$. The inverse of $$4$$ and $$7$$ are respectively: