What is the remainder when 6^17+17^6 divided by 7.
1>1
2>6
3>0
4>3

• ANS = 0
  
  1.(a+b)%m= (a%m+ b%m)%m
  2. ((qm+d)^n)%m = (d^n)%m , since in binomial expansion each term is divisible by m except last term
  
  so,
  (6^17 + 17^6)%7 = ((6^17)%7 + (17^6)%7) % 7
  =>((7-1)^17% 7 + (2*7+3)^6 % 7)) %7
  =>((-1)%7 + 729%7) %7 = (6+1)%7= 0
• 12 years agoHelpfull: Yes(18) No(1)
• use caculator for this type of questions, if the calculation gives you the answer which is of not decimal, then the reminder is 0. for thsi question the reminder is 0
• 12 years agoHelpfull: Yes(1) No(4)
• (7-1)^17/7 we get remainder -1
  2*7+
  3)/7 we remainder 3^17/7 we get remainder 1 so total 0
• 12 years agoHelpfull: Yes(0) No(1)
• any thing ^4 gives a unit digit 1 so
  [((6^4)^4)*6+((7^4)*49)]%7 we can write like this
  then
  [(1*6)+(1*49)]%7
  55%7=6
  so the ans is 6
• 12 years agoHelpfull: Yes(0) No(5)
• Arun, how can u tell that any thing ^4 gives a unit digit 1, can u explain ?????
  
• 12 years agoHelpfull: Yes(0) No(0)