Arthur Porges was an American author of numerous short stories most...

This paper tries to prove the following theorem: if you take any po...

Of course, the constraints $0\leq X_i \leq 9$ and $X_i$ integral fo...

It's not difficult to show that the G operator is not linear since ...

Note that: $$ G(10^n)=1^2+0^2 + \ldots +0^2 = 1 \\ G^2(13 \tim...

To prove $G(A)<A$ for $R \geq 4$ we observe that for a certain $R$,...

I encourage the Fermat's Library readers to try to polish the autho...

Surely it is not necessary to _repeatedly_ apply $G(\cdot)$ to $100...

Define $K_{k,b}(n)$ to be the sum of the $k$th powers of the ‘digit...