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Friday 8 February 2013

Remainder Problem

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

$$ N=2222^{5555}+5555^{2222} $$
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2 comments:

  1. ekaveera8 February 2013 at 23:14

    WE can use:

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

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

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

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  2. ekaveera8 February 2013 at 23:19

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

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

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