What is the remainder when 6^17 + 17^6 is divided by 7?
a)1
b)6
c)0
d)3

• remainder when 6^17 + 17^6 is divided by 7
  6^17mod7....>(7-1)^17mod7=(-1)^17(because 7^17 is divisible by 7 ,so we avoid it and only take (-1)^17 mod 7=-1 .........(1)
  17^6....>(7*2+3)^6 mod7=(3)^6 mod 7....729 mod 7=1 .......(2)
  so now remainder when 6^17 + 17^6 is divided by 7
  now eq (1)+(2) mod 7
  (6^17 + 17^6)mod 7=(-1+1) mod 7=0 mod 7=0
  ans c)0 is right(ans)
  
  
• 12 years agoHelpfull: Yes(42) No(17)
• simple answer is 0.. dont go lengthy just consider unit digits.
  6^17 unit digit = 6
  17^6 unit digit = 1
  6+1=7 which is divisible by 7
• 12 years agoHelpfull: Yes(15) No(57)
• Answer =a
  6^17 unit digit=6
  17^6 unit disit=9
  6+9=15 when 15/7 the remainder will be 1.
  
• 9 years agoHelpfull: Yes(3) No(2)