3 problems

The third nonlinear gcd conjecture. For sufficiently large $m$,

The first nonlinear gcd conjecture. For sufficiently large $m$,

Let $b\geq 2$ be an integer base, and let $(\alpha_1,\ldots,\alpha_n)$ be an $n$-tuple of real numbers. Writing their base-$b$ expansions in aligned columns, call the tuple normal…