What is reminder when 6^(17 )+ 〖17〗^6 is divided by 7?

• ans is 0
  
  it can be written as (7-1)^17=(-1)*(1-7)^17=-1-terms devided by 7=7-1=6
  and 17.....6 times devided by 7 gives remaider 9^3 again devided and gives 8 which finally gives 1.
  so (6+1)%7=0
• 12 years agoHelpfull: Yes(11) No(1)
• last digit of 6^17 is = 6^(4+4+4+4+1) equivalent to 6^1 ie 6
  similarly we can write 17^6=17^(4+2) equivalent to 17^2 ie 289
  now,
  289+6=295
  295/7 leaves remainder=1 , ans =1
• 12 years agoHelpfull: Yes(6) No(2)
• 80 percent
• 12 years agoHelpfull: Yes(3) No(10)
• ans is 1.....
• 12 years agoHelpfull: Yes(3) No(2)
• 6^17=6
  17^(4+2)=9
  6+9=15/7=1 REMAINDER
• 12 years agoHelpfull: Yes(2) No(0)
• it can be written as (7-1)^17=(-1)*(1-7)^17=-1-terms devided by 7=7-1=6
  and 17.....6 times devided by 7 gives remaider 9^3 again devided and gives 8 which finally gives 1.
  so (6+1)%7=0
• 12 years agoHelpfull: Yes(0) No(2)
• 0000...............
• 12 years agoHelpfull: Yes(0) No(2)
• reminder is 0000000
  
• 12 years agoHelpfull: Yes(0) No(3)