I found an interesting fact that every odd number can be written as
$(2^n-1)/A$ or $(2^n+1)/A$, where $n$ & $A$ are some integers.
If the odd number is $N$, then $n ≤ (N-1)/2$.
I have checked from $3$ to $101$ and it is true for all these odd numbers.
Is there a general proof for this odd number expression form?
Or a proof that this statement is wrong?