Question

when 5^99 is divided by 13 then the remainder is??

Answer 1

using the concept of mod..
25 is conguent to -1 mod 13(means when -1 is subtracted from 25 it is divisible by 13)
5^2 is congruent to -1 mod 13
=> 5^98 is congruent to -1 mod 13
=> hence, 5^98=13m-1
multiplying by 5.....5^99=13.5.m - 5
=> 5^99=13n -13 + 8
=> 5^99=13(n-1) +8
=> 5^99+13m + 8
=> Remainder = 8