what is the reminder when 6^17+7^16 is divided by 7

• (7-1)^17+7^16
  =[17c0(7)^17-17c1(7)^16(1)+17c2(7)^15(1)^2-.......+17c16(7)^1(1)^16-17c17(1)^17]+ 7^16
  in the expansion every term contains 7 which is divisible by 7 except the last term -17c17(1)^17=-1
  but remainder must be positive so 7-1=6...
  [for this lets consider previous term also 17c16(7)^1(1)^16-17c17(1)^17
  =17(7)-1=119-1=118
  when 118 devided by 7 leaves remainder 6...
  hence proved...]
  
• 12 years agoHelpfull: Yes(5) No(6)
• Answer is 0.Check out the latest post of the same question.
• 12 years agoHelpfull: Yes(3) No(0)
• as if 7^16 is divided by 7 it will give 0 remainder and when 6^17 is divided by 7 then the remainder will be 6 since 6 can be written as (7-1) and when(7-1)^ an odd number will be divided by 7 it will give 6 as remainder.so the total remainder=6.
• 12 years agoHelpfull: Yes(2) No(6)
• 6 is the right answer
  
• 12 years agoHelpfull: Yes(1) No(5)
• 6^17/7= 2
  7^16/7= 4
  6^17+7^16= 2+4= 6
  so ans is 6
• 12 years agoHelpfull: Yes(1) No(5)
• answer is 0 for sure...:):)....this same question was solved day before yesterday by our trainer of face institute...:):)
• 12 years agoHelpfull: Yes(1) No(1)
• (6^17 + 17^6)/7
  =((7-1)^17)/7 + ((17^(7-1) /7)
  =-1+1
  =0
• 10 years agoHelpfull: Yes(0) No(0)
• (6^17+7^16)/7 can be written as..........
  (6^17)/7 +(7^16)/7
  2nd term has Remainder=0.To get remainder from 1st term we can use a property of number system (ax-1)^n/a has remainder equal to (-1)^n.
  Here (7-1)^17/7 gives remainder equals to (-1)^17=-1.But remainder can not be negative.Hence remainder is 7-1=6.
  Ans. R=6
  
• 9 years agoHelpfull: Yes(0) No(0)