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