What is the remainder 6^17 + 17^6/7

• 6^17/7 =(7-1)^17/7=(-1)^17/7 = rem=> -1
  17^6/7 =(7*2+3)^6/7=(3)^6/7 =(27)^2/7=(28-1)^2/7=(-1)^2/7 => rem =1
  hence,remainder when 6^17+17^6 is divided by 7 is
  (-1)+1 = 0
  
  rem = 0
• 10 years agoHelpfull: Yes(29) No(4)
• to find the unit digit value first
  6^any value the unit digit will return only 6
  6^1=6,6^2=36 like that.
  7value cyclicity is 4 because unit digit is 7^1=7,7^2=9,7^3=3,7^4=1,7^5=7again it is repeated
  powervalue/cyclicity
  6/4 remain 2
  7^2 is 9
  so 6+9=15/7 remainder is 1.
• 10 years agoHelpfull: Yes(10) No(3)
• 6^17/7 is of the form a^n/a+1 so remainder will be 6
  n for second term 17^6/7=3^6/7 (after dividing by 7 3 will be d remainder)
  now remainder will be 1 as 8^2/7=1^2/7
  so 6+1=7 and 7/7=0
  o is the remaindr :)
• 10 years agoHelpfull: Yes(1) No(2)
• answer is 0
• 10 years agoHelpfull: Yes(0) No(5)