Latest TCS Aptitude Question SOLUTION: what will be the remainder when 7^81+7^6 is divided by 344??

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

Asked In TCS Triloki Shaw (11 years ago)

Solved Amit kumar jha Read Solution (7)

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Read Solution (7) :

Amit kumar jha  (11 years ago)

7^81+7^6/344
=7^81/344 +7^6/344
=(7^3)*27 /344+ (7^3)*2 /344
=343^27/344 + 343^2/344
=According to remainder theorem x^y/k
= (x-k)^y/k

=(-1)^27/344 + (-1)^2 /344
=-1+1
=0

Is this solution Helpfull? Yes (78) | No (1)  

palash verma  (11 years ago)

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.

Is this solution Helpfull? Yes (5) | No (6)  

MADHUSUDHAN K S  (11 years ago)

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

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subhash kumar  (11 years ago)

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.

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Guru Pranav  (11 years ago)

0 is the answer !!!

(-1)^27 + (-1)^2 = -1+1=0 Ans.

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Manisha Gupta  (11 years ago)

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

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Aalokanand jha  (8 years ago)

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

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