what will be the remainder when 7 81 7 6 is divided by 344

check cyclicity of remainder with powers of 7 it comes out to be 6
thus 81/6-> 3 as remainder means 3rd term or remainder when 7^3->343
also remainder when 7^6->1
add both remainders
1+343->344
which is again divisible by 344 therefore remainder is zero.
11 years agoHelpfull: Yes(5) No(6)
ACCORDING TO REMAINDER THEOREM.
R(A+B)/C=R(A/C)+R(B/C)
This implies the problem can be split into two
R(7^81/344)+R(7^6/344)
which can be rewritten as
R(343^78/344)+R(343^3/344)
Also according to remainder theory
R(A^n/B)=R(A/B)^n
hence it can be written as
(-1)^78+(-1)^3 = 0
11 years agoHelpfull: Yes(4) No(3)
since 7^3=343
7^81+7^6 = 7^6((7^75)-1)
here 75 in exactly divisible by 3. and After divided by 344, 7^75 gives remainder 1
so, ((7^75)-1) in exactly divisible by 344.
and we know that whatever we multiply with ((7^75)-1) is also exactly divisible
by 344.
Hence divided by 344, 7^6((7^75)-1) gives remainder 0.
11 years agoHelpfull: Yes(1) No(0)
0 is the answer !!!

(-1)^27 + (-1)^2 = -1+1=0 Ans.
11 years agoHelpfull: Yes(0) No(0)
In this type of questions simply do one thing just write the number as it is means write 7^81+7^6=78176 and then divide simply by 344 getting remainder = 0
11 years agoHelpfull: Yes(0) No(2)
7^81+7^6
(7^3)^27+(7^3)^2
(343)^27+(343)^2
(344-1)^27+(344-1)^2
(-1)^27+(-1)^2
-1+1=0
8 years agoHelpfull: Yes(0) No(0)

what will be the remainder when 7^81+7^6 is divided by 344??