Find the remainder when 97 ^97 ^ 97 is divided by 11?

did not get u pv aaditya.. :(

97^97^97 mod 11 = (-2)^97^97 mod 11

97^97 mod 5 = 2^97 mod 5 = (2^4)^24 * 2 mod 5 = 16^24 * 2 mod 5 = 2

Since 97^97 is odd, it is of the form 5k + 2 where k is odd.

So, -2^97^97 = -2^{5k+2} = -2^2 * -2^5k = 4*-32^k where k is odd

-32 mod 11 = 1

So, 4*-32^k mod 11 = 4*1 = 4