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

• 17^6 can also be return like (7*2+3)^6 in this (7*2)^6 is divided by 7
  so remaining 3^6/7 gives the reminder 1.....
  In 6^17/7 there is a formula that
  a^odd/a+1 gives remainder 6...
  a^even/a+1 remainder 1....
  from these reminder is 6.....
  total remainder is 6+1=7
  it is divided 7 gives remainder 0....
• 11 years agoHelpfull: Yes(24) No(0)
• ans=0, as 6^17/7 rem 6 and 17^6 rem 1 so on adding 0 will be remainder
  
• 11 years agoHelpfull: Yes(6) No(2)
• ans=0
  6^17/7=-1
  17^6/7=1
  1-1=0
• 11 years agoHelpfull: Yes(5) No(0)
• remainder 0
• 11 years agoHelpfull: Yes(1) No(0)
• reminder=0
• 11 years agoHelpfull: Yes(1) No(0)
• remainder 2
  
  [6^17]/7 => [(36)^(17/2)]/7 => [(35+1)^(17/2)]/7 = remainder 1
  [17^6]/7 => [(289)^3]/7 => [(287 =2)^3]/7 = remainder 1
  adding both remainder we get 2
• 11 years agoHelpfull: Yes(1) No(3)
• its 1 as 6^17 gives rem 6
  and 17^6 gives rem as 2
  6+2=8/7=1
• 11 years agoHelpfull: Yes(1) No(2)
• -1+1
  so ans is 0.
• 11 years agoHelpfull: Yes(1) No(0)
• (6^17 +17^6)/7=6/7+1/7=1
  so remainder=0
• 11 years agoHelpfull: Yes(1) No(0)
• 0
• 11 years agoHelpfull: Yes(0) No(0)
• we can solve it by concept of negetive remainder.
  in 6^17/7 we can take its remaindr as -1. and in 17^6/7=> 3^6/7 gives the remainder 1.
  so final ans is -1+1 = 0
  
• 11 years agoHelpfull: Yes(0) No(0)
• ans: 0
  (7-1)^17/7+(7*2+3)^6/7
  by negative remainder theorem:
  -1^17/7+3^6/7
  (6+1)/7
  remainder=0
• 11 years agoHelpfull: Yes(0) No(0)