Find the remainder when 3^101 is divided by 77.

1) 3
2) 47
3) 48
4) 9

• it can be solve by euler theorem..
  as 3, 77 r co-prime
  3^q(n)/77=1 where q(n)=77*(1-1/7)*(1-1/11)i.e 60
  3^60/77=1
  now remainder of(3^60*3^41)/77=remainder of (3^41)/77
  &as we know remainder of 3^4/77=4
  now reminder (3^41)/77=(3^40)*3
  reminder of 3^(4*10)*3/77=4^10*3/77
  reminder of 4^4*4^4*4^2*3/77= reminder of 256*256*48/77=reminder 25*25*48/77
  is samae as reminder of 9*48/77=47
  so ans reminder =47
• 11 years agoHelpfull: Yes(2) No(0)