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Q.
If $(11)^{27}+(21)^{27}$ when divided by $16$ leaves the remainder
Binomial Theorem
Solution:
[$a^{n}+b^{n}=(a+ b)(Q(a, b))$ if $n$ is odd
i.e. $a^{n}+b^{n}$ is divisible by $a+b$
if $n$ is odd
alternatively: interpret from $\left.(16-5)^{27}+(16+5)^{27}\right]$