Oh-oh,

acted sort of like a prime (sometimes). Sorry.

I'll try again, and if it's still not good, then I'll better stop and leave it for someone else.. I'm sorry for wasting your time if I made some mistakes again

(1)

(2)

(1),(2)

(3)

(1),(3)

; let

with

and

(4)

I left this part unchanged. And now:

Suppose

is even. This implies

and

odd, hence

is odd for every odd

. But

, so we get

for every odd

- impossible. This means that

must be odd.

. Having

and

, we get

, so

.

By induction, we show that

.

Suppose

. Then,

.

.

, where

.

.

is fixed arbitrarily and

, so

.

.