## Friday, 8 February 2013

### Remainder Problem

Find the Remainder when the number $N$ is divided by 7, where

$$N=2222^{5555}+5555^{2222}$$

1. WE can use:

$$2^6 \equiv 1(mod) 7$$

$$5^3 \equiv -1(mod) 7$$

$$1111 \equiv -2(mod) 7$$

2. Finally use, If
$$A \equiv r_1(mod)p$$ and
$$B \equiv r_2(mod)p$$ then

$$AB \equiv r_1r_2 (mod)p$$