Question

find the remainder when 103^52 is divided by 17​

Answer 1

Answer:

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 [6*6^10k / 11]

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

= 6 * 1

= 6