Question

find remainder 5^500/500

Answer 1

see the pic

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Answer 2

remainder = 1 for  5⁵⁰⁰/500

Step-by-step explanation:

5⁵⁰⁰/500

= 5³ * 5⁴⁹⁷ /500

= 125 * 5⁴⁹⁷ /500

=  5⁴⁹⁷ /4

= (4 + 1)⁴⁹⁷/4

(4 + 1)⁴⁹⁷  = 4⁴⁹⁷  +  ⁴⁹⁷C₁*4⁴⁹⁶*1  +...................................................+⁴⁹⁷C₄₉₆*4*1 + 1

= 4(4⁴⁹⁶ + ⁴⁹⁷C₁*4⁴⁹⁵*1  +...................................................+⁴⁹⁷C₄₉₆*1)  + 1

Hence when divided by 4

remainder = 1

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