Quote:
Originally Posted by petrw1
Thanks a lot....no big deal, but you dropped he 2x on line 2 of your napkin.

Yes, I know, thus the implication arrow afterwards, instead of an equality sign. Removing the 2 doesn't change the rest. If I were to get some fraction in the end, I could simply put it back. But it doesn't change the rationality, which is the whole question.
And, it isn't a napkin. (But I think you know that) It is my notebook I use for maths in the school. (BTW, I am graduating in May 2021, at least that's what I thought a year ago. Who knows what else might Covid take  we are learning online since the last Monday, and it's possible it will be until Christmas)
Quote:
Originally Posted by petrw1
So If I knew what I was doing I could reverse this process and get other whole numbers starting with √(x!+1) ??
x can be 4, 5, or 7.

Yes! Absolutely. You can shove in any number for x, even primorials, perfect powers, and also Riesel primes with even powers of base and square ks (based on few lookups, they might not exist), but sadly enough, no Mersenne primes except M2, as 2
^{p}  1 + 1 = 2
^{p}, which is not a square if the p is odd.

EDIT:
Silly me. Of course there can't be a Riesel prime with k being square and n being even, because of the almighty algebraic factors of a
^{2}  1 = (a1)(a+1)