6^17+17^6/7 what will be the remainder

• 6^17+17^6/7=((7-1)^17+(7*2+3)^6)/7=-1+((3)^6)/7=-1+((3^3)^2)/7=-1+((28-1)^2)/7
  so remainder vll be -1+(-1)^2=-1+1=0
• 11 years agoHelpfull: Yes(21) No(6)
• answer is 0
  solution:
  (6^17+17^6)/7
  (-1)^17 + (3)^6
  -1 + (3^2)^3
  -1 + 2^3
  -1 + 1 => 0
• 11 years agoHelpfull: Yes(3) No(0)
• since a^n/(a+1)=a when n is odd
  and (ax + 1)^n /a =1 for any value of n
  so 6^17/7= 6 and 3^6/7=729/7=(728+1)/7=(7*104+1)/7=1
  i.e 6+1/7=7/7=0
  hence remainder is 0
• 11 years agoHelpfull: Yes(3) No(3)
• 6-3=3
  6^17 will make a remainder of 6
  and 17^6/7 will make remainder of -3
  so total remainder is 3
• 11 years agoHelpfull: Yes(2) No(4)
• r(6^17)=6;
  r(7^6)=3;
  6+3=9/7;
  r(9/7)=2;
• 11 years agoHelpfull: Yes(1) No(1)
• if the ques is (6^17+17^6)/7, then we can write ((7-1)^17)/7+(14+3)^6/7
  =-1^17/7+(3^2)^3/7
  =(-1/7)+(7+2)^3/7
  =-1/7+8/7
  so rem is -1+1=0 ans.
• 11 years agoHelpfull: Yes(1) No(0)
• 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
  
• 11 years agoHelpfull: Yes(1) No(0)
• answer is zero
  solution :
  [ (7-1)^17 ] / 7 + [ ( 14+3) ^ 6 ] / 7
  -1 ^ 17 + (3^6) / 7
  -1 + [3^(2*3)] / 7
  -1 + (9^3) / 7
  -1 + ( 2^3) / 7
  -1 + 8/7 = -1 + 1 = 0 :)
  
• 9 years agoHelpfull: Yes(1) No(0)
• ans is 2
  6^7/7 reminder is -1
  17^6/7 reminder is 3
  then 3-1 = 2
• 11 years agoHelpfull: Yes(0) No(7)
• plz any one tell clear explantion
  
• 11 years agoHelpfull: Yes(0) No(0)
• ((6^2)^8*6)/7 +(17^6)/7
  ((36)^8*6)/7+(3)^6
  (1)^8*6+729
  6+729
  735
  
• 11 years agoHelpfull: Yes(0) No(0)
• dear admin......plz explain the solution clearly.......
• 11 years agoHelpfull: Yes(0) No(0)
• ans is: 6+1 =7
  logic: according to "FERMATS RULE" we can do
  ie...if gcd(a,p)=1 then a^(p-1)=1mod(p)
  here p is 7 and we have to calculate indivisual
• 11 years agoHelpfull: Yes(0) No(1)
• 0 7
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
• 10 years agoHelpfull: Yes(0) No(0)
• 0 is the answer because
  
  6^7mod7 can be written (7-1)^7 mod 7=-1
  17^6mod7 can be written (7*2+3)^6mod7=3^6mod7=729 mod7=1
  
  -1+1=0
• 10 years agoHelpfull: Yes(0) No(0)