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

• 6 ^ 17 / 7 => (7-1)^7 / 7 => (-1)^7 => rem = -1
  
  17^6 / 7 => (2*7+3)^6 / 7 => 3^6 / 7 => 27*27 / 7 => -1*-1 / 7 => 1/7 => rem = 1
  
  so, 6 ^ 17 + 17 ^ 6 / 7 => rem(-1 + 1)/ 7 => 0
  
• 10 years agoHelpfull: Yes(11) No(0)
• Unit digit approach can not be applied in remainder theorem.
  By sequence method
  6^17 remainder will be 6 or -1
  17^6 remainder will be 1
  so overall remainder=-1+1=0 ans.
• 10 years agoHelpfull: Yes(7) No(0)
• reminder is 0
• 10 years agoHelpfull: Yes(1) No(2)
• Unit digit in 6 ^ 17 is 6 and in 17 ^ 6 is 9.
  Thus, (6+7)/7=13/7 has remainder 6.
  Ans is 6.
• 10 years agoHelpfull: Yes(1) No(7)
• **SORRY**
  (6+9)/7=15/7 has remainder 1.
  Ans is 1.
• 10 years agoHelpfull: Yes(1) No(8)
• soln will be 0
  
• 10 years agoHelpfull: Yes(0) No(1)
• remainder is 0
  in 6^17 divided by 7 remainder is (-1)^17 17 is odd so remainder is -1
  and in 17^6 divided by 7 remainder is 3^6=(3^3)^2=27^2 then remainder is (-1)^2 2 is even so remainder of 17^6 divided by 7 is 1
  finally 6^17+17^6 remainder is -1+1=0
  so reminder of this equation is 0;
• 10 years agoHelpfull: Yes(0) No(0)
• What's the correct approach friends?
• 10 years agoHelpfull: Yes(0) No(0)
• 6*6^16+17^6/7
  
  6*36^8+3^6/7
  
  6*1^8+9^3/7
  
  6+2^3/7
  
  14/7
  
  remainder 0
• 10 years agoHelpfull: Yes(0) No(0)
• answer:1
  because : 6^17 unit place will be 6 and 17^6unit place will be 9 total 6+9=15/7remainder 1
  
• 8 years agoHelpfull: Yes(0) No(0)