I was asked to show the binary form of $2^{2^5}+1$ and then to convince that the number equals 4 294 967 297 in decimal.
it is pretty easy to show that $2^{2^5}+1 = 2^{32} + 2^0$ and therefore the binary form will be 1 in the most right place and a bunch of zeros till the 32th place from the left, where another 1 comes due to the fact that these ones are the coefficients of the twos in this writing form.
I thought that in order to show that the enormous decimal equals to $2^{2^5}+1$ one can convert it to its binary form in "the traditional way" and show the equality of the two binary forms, however that will take ages and a lot of writing..
is it really the single way so show it? im looking for smarter way
Thanks in advance