Find the remainder when 7^103 is divided by 24
Solution) we know by the concept of mod that.....
49 is congruent to 1 mod 24(means if 1 is subtracted fom 49 u get 48 which is divisible by 24)
so 7^2congruent to 1 mod 24
so 7^102congruent to 1 mod 24(raising to the power 51)
hence the remainder when 7^102 is divided by 24 is 1 i.e. 7^102=24m+1
so multipling by 7 both sides we have....7^103=24.7m+ 7
hence 7^103=24n + 7
so remainder is 7 (ans)