what will be the remainder when 6^17+17^6 is divided by 7?

• {(7-1)^17 + (287+2)^3}%7
  ={(-1)^17 + 2^3}%7
  =(-1+8)%7
  =0
  so remainder is 0
  
  
• 12 years agoHelpfull: Yes(1) No(2)
• hey this is the method to find remainder of these que.
  we can write 6 as(7-1) so if we explain (7-1)^17 in nCr series then last term will be 17C17*(-1)^17=-1 and remains will be divided by 7 so remainder for this is -1 and similarly we can write 17^6=(17^2)^3=(289)^3=(287+2)^3 which will have last term as 3C3*2^3=8=7+1(since 287 is divisible by 7), so it gives remainder 1.
  then final remainder is -1 + 1=0
• 12 years agoHelpfull: Yes(1) No(0)
• 6/7 remainder= -1
  17/7 remainder= 3
  =>6^17+17^6 is divided by 7
  =>(-1)^17+3^6 is divided by 7
  =>(-1+729)/7
  => 728/7 => quotient is 104 and remainder is 0.
  
• 11 years agoHelpfull: Yes(1) No(0)
• plz explain clearly
  
• 12 years agoHelpfull: Yes(0) No(0)