Question

what will be the remainder when 50^(51^52) is divided with 11​

Answer 1

Answer: 6

We need to find out Rem [50^51^52 /11] = Rem [6^51^52 /11]

Now, by Fermat's theorem, which states Rem [a^(p-1)/p] = 1, we know

Rem [6^10 /11] = 1

=> Rem [6^10k / 11] = 1

The number given to us is 6^51^52

Let us find out Rem[Power / Cyclicity] t0 find out if it 6^(10k +1) or 6^(10k +2). We can just look at it and say that it is not 6^10k

Rem [51^52 / 10] =1

=> The number is of the format 6^(10k + 1)

Now, we need to calculate Rem [6^51^52 /11]

= Rem [ 6^(10k + 1) / 11]

= Rem [6x6^10k / 11]

= Rem[6/11] x Rem [6^10k / 11]

= 6 x 1

= 6 _______(Ans.)

Hope it helps. ^_^

Thanks!