Question

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

• A. 0
• B. 1
• C. 2
• D. 14

Answer 1

Answer: (A)

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