what remainder comes (6)^17+(17)^6 is divisible by 7

• (6^17+17^6)/7
  ={(-1^17)+(3^6)}/7
  =(-1+729)/7
  =728/7
  Remainder is zero
• 12 years agoHelpfull: Yes(1) No(0)
• (6)^17+(17)^6
  =(7-1)^17+(14+3)^6
  =17C0(7)^17 + 17C1(7)^16*(-1)^1 + 17C2(7)^15*(-1)^2 + .... + 17C17(-1)^17
  + 6C0(14)^6 + 6C1(14)^5*(3)^1 + .... + 6C6(3)^6
  Now all the terms except 17C17(-1)^17 and 6C6(3)^6 are divisible by 6
  So reminder will be same as when sum of 17C17(-1)^17 = -17 and 6C6(3)^6 = 729 is divided by 7
  i.e., (729-17)/7 = 717/7
  Reminder is 5
• 12 years agoHelpfull: Yes(0) No(1)