Question

what is the remainder if 2^32+1 is divided by 2^9+2^7+1?

Answer 1

(2^32+1)/(2^9+2^7+1) =4294967296+1/ 512+128+1
= 4294967297/641

The number is divisble so no reminder.

Answer 2

You can siply take logarithm up and down
$\frac{log_{10}2^{32}+log_{10}1}{log_{10}2^9+log_{10}2^7+log_{10}1}$
⇒$\frac{log_{10}2^{32}}{log_{10}2^9.2^7}$
⇒$\frac{32log_{10}}{log_{10}2^{9+7}}$
⇒$\frac{32log_{10}2}{16log_{10}2}$
⇒$\frac{32}{16} =2$