what is the remainder for 6^17+17^6 by dividing with 7 ?

• ans is:0
  6^2 on dividing by 7 gives remainder 1
  6^3 gives remainder 6
  6^4 gives remainder 1
  similarly,6^17 gives remainder 6
  17^6 = 24137569 , which on dividing by 7 gives remainder 1.
  therefore 6+1=7
  7 is completely divisible by 7
  Hence ,remainder is 0.
• 11 years agoHelpfull: Yes(28) No(2)
• 2*6*17/7 =>6*6/7 =>36/7 =>1 is the remainder
• 11 years agoHelpfull: Yes(6) No(0)
• 0 is the answer
• 11 years agoHelpfull: Yes(3) No(1)
• 0 since the expression reduces to 735 mod 7
• 11 years agoHelpfull: Yes(2) No(1)
• 5
  
  6^2 gives a remainder 1
  => 6^16 gives a remainder 1
  => 6^17 gives a remainder 6 when divided by 7
  
  17^3 gives a remainder -1
  => 17^6 gives a remainder = -1 = 7 - 1 = 6
  
  => Remainder = 6 + 6 = 12 = 5
• 11 years agoHelpfull: Yes(1) No(7)
• we can write it as 36^17/2 + (14+3)^6
  => (35+1)^17/2 + (3)^6
  
  //(x+r)^n=C0*x^n + C1*x^(n-1)*r + C2*x^(n-2)*r^2+......+r^n//
  =>(1^17/2)+(9^3)
  =>1+(7+2)^3
  =>1+2^3
  =>1+8
  =>7+2
  so ans is 2
• 11 years agoHelpfull: Yes(1) No(2)
• 3. two squares of length one unit, one square of diagonal length one unit
• 11 years agoHelpfull: Yes(0) No(3)
• 6^17=6*(7-1)^16 rem=6
  17^6=(287+2)^3 rem=2^3=8 287/7=rem 0
  rem=6+8=14
  so final rem 14/7 rem=0..........
• 11 years agoHelpfull: Yes(0) No(4)
• 6^17=6
  17^6=1
  6+1=7/7=0
  so the remainder is 0
  
• 11 years agoHelpfull: Yes(0) No(2)
• remainder= 0
• 11 years agoHelpfull: Yes(0) No(1)