Question : What will be the remainder when $27^{27}+27$ is divided by 28?
Option 1: 28
Option 2: 27
Option 3: 25
Option 4: 26
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Correct Answer: 26
Solution :
$27^{27}+27$ can written as $27^{27}+1^{27}-1+27=(27^{27}+1^{27})+26$
We know that A
n
+ B
n
is divisible by A + B when n is odd.
Here n = 27 is an odd number.
When $(27^{27}+1^{27})$ is divided by 28, the remainder will be 0.
And, when $(27^{27}+1^{27})+26$ is divided by (28), the remainder will be 26.
Hence, the correct answer is 26.
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