Remainder of (6^17+17^6)/7= ?

• 6^17/7 = (7-1)^17/7 => (-1)^17/7 = -1/7
  
  17^6/7 = (2*7+3)^6/7 = 3^6/7 = 27^2/7 =(4*7-1)^2/7 =(-1)^2/7 = 1/7
  
  so, (6^17+17^6)/7 = (-1+1)/7 => 0/7 rem = 0
  
• 10 years agoHelpfull: Yes(26) No(2)
• ans = remainder =0
  6^17+17^6 = (7-1)^17 + (21-4)^6 = (7-1)^17 + (7*3 -4)^6
  therefore we need to condider (-1)^17 + (-4)^6
  (-1)^17= -1
  and
  (-4)^6= 4^6=4096
  when 4096/7 remainder= 1
  so add all the remainders==>> therefore -1+1= 0
  ans is 0.
• 10 years agoHelpfull: Yes(2) No(2)
• please anyone tell me about verbal part??
• 10 years agoHelpfull: Yes(1) No(0)
• love u rakesh
  
• 10 years agoHelpfull: Yes(1) No(0)
• when 6^17/7 gives u -1/7
  at the same time 17^6/7 gives u 8*2+1/7 which can be taken as =+1/7
  on finalising -1+1/7 gives u 0
  
  y can't we take like this
• 10 years agoHelpfull: Yes(0) No(1)
• 17%7=3
  3^6%7= (9%7)^3 =(2^3)%7
  8%7=1
  
  & the first 6 will be added to 1
  s0 7/7.. remainder 0
• 10 years agoHelpfull: Yes(0) No(0)