3 problems

Let $k>3$, and let $F^{(k)}=(F_n^{(k)})_{n\geq 2-k}$ be the $k$-Fibonacci sequence defined by … for $n\geq 2$, with $F_{-(k-2)}^{(k)}=\cdots=F_0^{(k)}=0$ and $F_1^{(k)}=1$. A repdi…

Repdigit Niven-number parametrization conjecture. The solutions of the repdigit Niven-number equation are parameterized by

A triangular number is a number of the form $T_n=n(n+1)/2$ for a positive integer $n$, and a decimal representation consists of a single repeated digit when all its digits are equa…