Q. What is the reminder of 6^17+17^6 is divided by 7?

• 6^17+17^6
  =(7-1)^17 +(14+3)^6
  dividing by 7 then for reminder
  -1^17 + 3^6
  =728/7
  =104 So, reminder =0
• 11 years agoHelpfull: Yes(37) No(2)
• Ans : 0
  6^17/7 =(7-1)^17/7=(-1)^17/7 gives rem= -1
  17^6/7 =(7*2+3)^6/7=(3)^6/7 =(27)^2/7=(28-1)^2/7=(-1)^2/7 gives rem =1
  hence,remainder when 6^17+17^6 is divided by 7 is
  (-1)+1 = 0
• 11 years agoHelpfull: Yes(20) No(0)
• 6^17/7+17^6/7
  for 6^17 remainder is 6 and for 17^6 remainder is 1
  so 6+1/7=1 so resultant remainder =0
• 11 years agoHelpfull: Yes(12) No(3)
• 6^7=unit place digit 6 & 17^6=unit place digit is 9
  9+6=15
  15/7 gives remainder=1
  So answer is 1
• 10 years agoHelpfull: Yes(6) No(3)
• In order to solve such remainder problems try to get the form ((aN + 1)^x)/N or ((aN-1)^x)/N where a and x are any numbers
  when this form is attained we can replace it by (-1)^x or (1)^x respectively.
  here 6^17 + 17^6 /7 can be separated as 6^17/7 + 17^6/7
  = (7-1)^17/7 + (35-1)^6/7
  = -1^17 + -1^6
  = -1 + 1
  = 6 + 1
  = 7
  since 7 is >= the denominator so we further divide it by 7
  = 0
• 11 years agoHelpfull: Yes(5) No(5)
• the final digit obtained by solving the above expression is 304 so when u divide that number with 7 the remainder is 3
  so the remainder is 3
• 11 years agoHelpfull: Yes(2) No(3)
• the remainder is 2.
  as,,(6^17 + 17^6)=(7-1)^17 +(14+3)^6
  the actual remainder will be for (-1)^17 + (3)^6 = 1+ 729 = 730
  so, 730/7 remainder is 2
  so the answer is 2
• 11 years agoHelpfull: Yes(2) No(2)
• reminder of 15/7=1
  so ans is 1
• 11 years agoHelpfull: Yes(1) No(1)
• POWER CYCLE OF 6 IS 6...Hence the unit digit is 6..and the power cycle of 7 in 17 is 9..hence 6+9/7=1
• 10 years agoHelpfull: Yes(1) No(1)
• reminder=0
• 10 years agoHelpfull: Yes(1) No(0)
• 6^17+17^6
  (7-1)^17+(7+10)^6
  -1^17+10^6
  -1+10^6
  -1+(7+3)^6
  -1+(3^2)^3
  -1+2^3
  -1+1^6; remainder=0
• 10 years agoHelpfull: Yes(1) No(0)
• 6^17+17^6=(7-1)^17+(14+3)^6
  then reminder for 7 is (1^17+3^6)/7
  =730/7
  reminder = 2
• 11 years agoHelpfull: Yes(0) No(1)
• the remainder is 0.
  (6^17 + 17^6)/7 = (6^17)/7 + (17^6)/7
  the remainder for (6^17)/7 is 6 and the remainder for (17^6)/7 is 1.
  when they are added we get 7... the remainder for 7/7 is 0
  so the answer is 0
• 11 years agoHelpfull: Yes(0) No(0)
• (6^2*6^2*6^2*6^2*6^1)+(17^2*17^2*17*2)=4
• 11 years agoHelpfull: Yes(0) No(0)
• 6^17+17^6
  easy method = first we need to find reminder to make digit small digit make 1
  6divide by 7 =reminder is -1
  so it become
  (-1)^17=-1
  now see second part = 17^6
  find reminder of 17divide by 7 = 3
  (3)^6
  again 6 divide 7 = -1
  it become
  (3)^-1= 1/3
  reminder of 1/3=1
  
  so -1+1 = 0 answer
  
  
• 11 years agoHelpfull: Yes(0) No(0)
• 6^17+17^6
  (7-1)^17+(7+10)^6
  -1^17+10^6
  -1+10^6
  999999/7 remainder=0
• 10 years agoHelpfull: Yes(0) No(3)
• ans =1
  6^17+17^6 = 6^(4*4+1) + 17^(4*1+2) = 6^1 + 17^2
  Now we check the units place we get , 6 and 9 for 6^1 and 17^2
  6+9=15/7 remainder is 1
• 10 years agoHelpfull: Yes(0) No(0)
• 6^something=6
  17^6=9
  6+9/7=1
• 10 years agoHelpfull: Yes(0) No(1)
• 6^17=6*36^8 now 6*36^8+17^6/7=6*1^8+3^6/7 now 3^6=^3 noe 6+9^3/7=6+2^3/7=14/7 remainder 0 by using remainder theorem...
• 10 years agoHelpfull: Yes(0) No(0)
• ans is 2
  bcoz remainder of 6^17 is 6
  remainder of 17^6 is 9
  
  (7+9)/7= remainder 2
  
• 10 years agoHelpfull: Yes(0) No(0)
• Please give the Admin Solution for these question?
• 9 years agoHelpfull: Yes(0) No(0)
• unit digit of 6^17 is 6 and unit digit of 17^6 is 9.
  so 6+9=15
  15/7 gives remaider 1 .so ans is 1
• 9 years agoHelpfull: Yes(0) No(0)
• first step (7-1)^17+(14+3)^6
  now divide this equation by 7 u will got
  (-1)^7+(3)^6
  (-1+729)/7
  728/7
  104 so remainder =0 answer
• 9 years agoHelpfull: Yes(0) No(0)
• 6^17%7=( -1)^17 = 6
  17^6%7=3^6%7=3^2^3%7=2^3%7=1
  1+6=7%7=0
• 9 years agoHelpfull: Yes(0) No(0)