what is remainder when 6^17 +17^6isdividedby7?

• It is divisible by 7, so rem will be 0.
  for 6^17/7=(-1)^17/7=-1
  Rem cant be a negetive. so 7-1=6 is rem.
  for 17^6/7=(3)^6/7=(27)^2/7=(-1)^2/7=1/7
  So rem for second part is 1.
  if we add both rems
  6+1=7 i.e. absolutely divisible by 7. so rem will be 0
  
  
  
• 10 years agoHelpfull: Yes(14) No(5)
• 0(ans)
  6^17/7=(7-1)^17/7 = (-1)^17/7 = -1
  rem is -ve so 7-1=6 is rem.
  for 17^6/7 = (14+3)^6/7 = (3)^6/7 = (9)^3/7 = (7+2)^3/7 = (2)^3/7 = (8)/7
  (7+1) /7= 1/7
  so rem for 2nd part is =1 and of 1st part is =6
  total rem. = 1+6=7
  so 7/7=0
• 10 years agoHelpfull: Yes(6) No(1)
• 6^(x) unit digit 6
  17^(6)= 1st time 17*17=unit digit -9
  and next unit digits are 3,1,7,9
  so 6+9=15
  15/7=1 remainder
• 10 years agoHelpfull: Yes(3) No(1)
• it can be solved as:
  [(7-1)^17+(14+3)^6]/7=[(-1)^17+(3)^6]/7=-1+[(3^2)^3]/7=-1+1=0
  
• 10 years agoHelpfull: Yes(0) No(0)
• (7-1)^17+(14+3)^6
  =(-1)^17+(3^3*3^3)
  =-1+(28-1)*(28-1)
  =-1+(-1*-1)
  =0/7
  Remainder 0
• 10 years agoHelpfull: Yes(0) No(0)