Question

find the remainder when 5^99 is divided by 13

Answer 1

Answer is 8

Explanation 1:  

52≡25≡12≡−1mod1352≡25≡12≡−1mod13

⟹599≡52∗49+1≡((52)49×51)≡((−1)49×5)≡(−5)≡(13−5)≡8mod13⟹599≡52∗49+1≡((52)49×51)≡((−1)49×5)≡(−5)≡(13−5)≡8mod13

Therefore  599≡8mod13599≡8mod13  

Answer 2

1 remainder hope it works