Question

Find the remainder when 7^¹⁰³ is divided by 24.

Answer 1

Solution-: W will solve it by using mod method

7^(103) divisible by 24

so we get
49 is congruent to 1 mod 24

So it means
7^2congruent to 1 mod 24

7^102congruent to 1 mod 24 becaise 7^2*(51) = 7^102

So we can say remainder when 7^102 is divided by 24 is 1
It means
7^102=24m+1
Now we will multiply both sides by 7 we get
7^102 *7 = 24*7m+7
7^103 = 24*n +7 (suppose 24m*7 = 24*n )
It means remainder is 7
So our answer will be 7