What is the remainder when 617+1176 is divided by 7?
A. 1
B. 6
C. 0
D. 3

• actually the question is 6^17+117^6
• 9 years agoHelpfull: Yes(18) No(3)
• answer is 1.simple..617+1176=1793/7..remainder 1
• 11 years agoHelpfull: Yes(11) No(18)
• 1st: 6^17=6^(16+1)=6*6^16=6*36^8
  now rem(6/7)*rem(36/7 * 36/7 * 36/7 *... 8 times)=(-1)*(1*1*1*...8 times)= -1
  2nd: rem(117^6/7)= rem(117/7 * 117/7 * 117/7* ... 6 times)= rem((-2)^6/7)=rem(64/7)=1
  now just add up 1st and 2nd
  -1 + 1=0
  so, reminder is " 0 "
• 8 years agoHelpfull: Yes(5) No(2)
• if the qstn is 6^17+117^6..dn the ans is 0
• 8 years agoHelpfull: Yes(3) No(0)
• 6793/7=256 and rem=1
  ans=1
  
• 11 years agoHelpfull: Yes(2) No(4)
• Question is: What is the remainder when 617+1176 is divided by 7?
  Ans:617 = (7−1)17 =
  17C0.717−17C1.716.11.....+17C16.71.116−17C17.117
  
  If we divide this expansion except the last term each term gives a remainder 0. Last term gives a remainder of - 1.
  
  Now From Fermat little theorem, [ap−1p]Rem=1
  So [1767]Rem=1
  
  Adding these two remainders we get the final remainder = 0
• 9 years agoHelpfull: Yes(2) No(2)
• The actual question is What is the remainder when 6^17 + 117^6 is divided by 7??
  Can anyone solve it???
  
• 9 years agoHelpfull: Yes(2) No(0)
• 617 +1176 /7
  sol= 617/7 +1176/7
  =(1+0)/7=1 is the remainder...
• 11 years agoHelpfull: Yes(1) No(4)
• actually the question is 6^17+117^6
• 9 years agoHelpfull: Yes(1) No(0)
• Sorry my answer was correct.
  But actually question is: What is the remainder when 6^17+117^6 is divided by 7?
• 9 years agoHelpfull: Yes(1) No(0)
• Please anyone explain it clearly. and i think question was wrong
• 9 years agoHelpfull: Yes(0) No(0)
• (88x7)+1+(168x7)
  so,remainder 1
• 9 years agoHelpfull: Yes(0) No(1)
• A.1
  1793/7
  remainder=1
• 8 years agoHelpfull: Yes(0) No(1)
• 617+1176=1793 & 1793/7....remainder 1
• 8 years agoHelpfull: Yes(0) No(1)
• 617+1176=1793 it divided by 7 than remainder is 1
• 8 years agoHelpfull: Yes(0) No(1)
• 1176+617=1793%7=1
• 8 years agoHelpfull: Yes(0) No(0)
• 6^17+(117)^16
  First took 6^17 ,
  we can split 6^17 as = 6^(16+1)
  =6*(6)^16
  =6*((6)^2)^8
  =6*(36)^8
  divide this by 7 =6/7 *(36/7*..... upto 8times)
  6/7 as 6 =mod 7 => -1
  35/7 as 35 = mod 7 => 1
  so the first one gets -1.
  similarly calculate the second (117)^6 = (117)*(117)^5
  =(117/7)*(117/7*..upto 5times)
  =(5)*(5*.... upto 5times)
  =15625/7 =1
  -1+1=0
• 3 years agoHelpfull: Yes(0) No(0)