6^17+17^6 when divided by 7. What is the remainder?

• 6^17mod7....>(7-1)^17mod7=(-1)^17(because 7^17 is divisible by 7 ,
  
  
  
  (-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
  
  0 remainder
• 12 years agoHelpfull: Yes(28) No(1)
• sorry by mistake
  
  6^17+17^6
  (6^16)*6 + (3)^6 when 17 divided by 7 remaindr is 3
  (36^8)*6 + 27^2 when 36 and 27 divided by 7 remaindr is 1 and 6 respectively
  (1^8)*6 + 6^2
  6 + 36=42
  divided by 7 we get 0 remaind
• 12 years agoHelpfull: Yes(3) No(4)
• 0
  is the answer
• 12 years agoHelpfull: Yes(2) No(2)
• Remainder is zero when 6^17+17^6 is divided by 7.
• 12 years agoHelpfull: Yes(1) No(2)
• 6^17+17^6
  (6^16)*6 + (3)^6 when 17 divided by 7 remaindr is 3
  (36^8)*6 + 27^2 when 36 and 27 divided by 7 remaindr is 1 and 6 respectively
  (1^8)*6 + 6^2
  6 + 36=42
  divided by 7 we get 1 remaindr
• 12 years agoHelpfull: Yes(1) No(11)
• 0 is the ans.
  because 6^17 leaves "6" as remainder and 17^6 leaves 1. sum of the remainders is 7 and 7%7=0
  
• 12 years agoHelpfull: Yes(1) No(2)
• 6^17+17^6/7
  for find the reminder..firstly
  6^17/7+17^6/7
  then..solve this..power term 17,6 is divided by 6 & without power term 6,17 is divided by 7..then reminder is..
  6^5/7+3^0/7
  then...7776/7+1/7..solve this..then
  6+1/7..& answer is reminder 0....
  
• 12 years agoHelpfull: Yes(1) No(1)
• ans is 0
  ....
  bcz 6^17 divided by 7 remender is 6
  then 17^6 divided by 7 remender is 1
  then 6+1 divided by 7 then remender is 0
• 12 years agoHelpfull: Yes(1) No(1)
• remainder:0
• 12 years agoHelpfull: Yes(1) No(0)
• answer is 0.
• 12 years agoHelpfull: Yes(1) No(0)
• 6^17+17^6
  (6^2)^8*6+(14+3)^6
  (1)^8*6+3^6
  6+(3^2)^3
  6+2^3
  6+1
  7
  so remainder is 0;
  
• 12 years agoHelpfull: Yes(1) No(2)
• @atul can this method is applicable to any such questions? or only when divided by 7?
• 12 years agoHelpfull: Yes(0) No(1)
• 6^17=((6^2)^8)*6= (1^8)*6=6........... 1 is reminder
  17^6= 3^6.................. 3 is reminder
  = 9^3= 2^3=8...........
  6+8=14
  14%2=0
  so ans is 0
  
• 12 years agoHelpfull: Yes(0) No(0)