Find the remainder when 50^56^52 is divided by 11? Plzz explain the procedure..as im not sure of the answer...

1) 2
2) 3
3) 4
4) 5

• 50^56^52=50^.....6 i.e.some number ending in 6 as unit's digit[since all powers of 6 end in 6 as unit's digit.
  Now, 50^....6 can be written as (50^.....0)*(50^6) [simple addition of exponents]
  By Fermat's Little Theorem, we know that (a^(p-1))/p=1 when a and p are co-prime and p is a prime number.
  Here, 50 and 11 are co-prime ans 11 is a prime number.
  Hence, 50^10/11=1 or 50^(10*n)/11=1 where n is any positive integer.
  Applying this particular principle here,
  50^.....0=1
  This leaves 50^6/11
  =rem[50*50*50*50*50*50/11]
  =rem[6*6*6*6*6*6/11]
  =rem[36*36*36/11]
  =rem[3*3*3/11]
  =rem[27/11]=5
  Thus, answer is 5.
• 10 years agoHelpfull: Yes(3) No(0)