Question

If $(11{)}^{27}+(21{)}^{27}$ when divided by $16$ leaves the remainder

Answer 1

Answer: 0

[$a^n+b^n=(a+b)(Q(a,b))$ if $n$ is odd
i.e. $a^n+b^n$ is divisible by $a+b$
if $n$ is odd
alternatively: interpret from $(16-5{)}^{27}+(16+5{)}^{27}]$