remainder of 6^17+17^6 when divided by 7

• Split the above expression in two parts :-
  
  (6^17)/7 + (17^6)/7
  
  Now 6 when divided by 7 gives remainder 6 or -1, so we can write
  (6^17)/7 = (-1)^17 = -1
  
  Also
  17 when divided by 7 gives remainder 3
  So we can write it as (3^6)/7
  Using cycle of 3 we can find the remainder of above term as:-
  
  3 / 7 remainder= 3
  3^2 / 7 remainder= 2
  3^3 / 7 remainder= 6
  3^4 / 7 remainder= 4
  3^5 / 7 remainder= 5
  3^6 / 7 remainder= 1
  
  So final answer will be (-1 + 1) = 0 ans
• 11 years agoHelpfull: Yes(27) No(2)
• given (6^17)/7+(17^6)/7
  reminder= ??
  so first divide 6 by 7 we get either 6 or -1
  and when 17 is divided ,rem=3
  after continuing it we have -1+1=0 ans
• 11 years agoHelpfull: Yes(3) No(7)
• 6^17)/7 = (-1)^17 = -1
  3^6 / 7 remainder= 1
  (-1 + 1) = 0 ans
• 11 years agoHelpfull: Yes(1) No(0)