wht is reminder when 6^17+17^6 is devided by 7?

• 6^17 mod 7=(7-1)^17 mod 7
  so 7^17 divide by 7, middle term divide by 7 and remainder will 0,so we only take (-1)^17 mod 7=-1
  2) 17^6 mod 7=(7*2+3)^6
  so now (7*2)^17 divide by 7 and remainder will 0,so we only take (3)^6 mod 7=
  729 mod 7=1
  now add (1)+(2)
  -1+1=0(ans
  
• 12 years agoHelpfull: Yes(18) No(0)
• (7-1)^17 + (7*2+3)^6
  binomial theorem
  -1+3^6=728
  728%7=0
• 12 years agoHelpfull: Yes(2) No(2)
• remainder when 6^17=6
  and when 17^6=1
  so the reamainder will be (6+1)/7=0
• 12 years agoHelpfull: Yes(2) No(1)
• Answer: 0
  
  6^17 = 6^4 * 6^4 * 6^4 * 6^4 * 6
  17^6 = 17^2 * 17^2 * 17^2
  
  (6^4)/7 gives remainder 1
  6/7 gives remainder 6
  so 1*1*1*1*6 = 6 . this is the remainder part of 6^17.
  like wise (17^2)/7 gives remainder 2.
  so 2*2*2 = 8 . this is the remainder part of 17^6.
  6^17 + 17^6 = 6 +8 = 14 . 14/7 gives remainder 0.
• 12 years agoHelpfull: Yes(2) No(0)