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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 $(16-5)^{27}+(16+5)^{27}$