5 problems

Generalized Collatz convergence and cycle conjecture. For all $p\geq0$ with $p\ne2$, the triplet $(2^{p+1},3\times2^p,2^p)_+$ is strongly admissible of order one, with unique trivi…

Mersenne-triplet admissibility conjecture. For all $p\geq 2$, $(2^{p-1},2^{p}-1,1)_{\pmb{+}}$ is an admissible triplet of order one. It is strongly admissible only for $p=2$ and we…

Let $\mathcal{G}$ be the Lie group of nonlocal symmetry diffeomorphisms associated with the integrable map … . Let its Lie algebra of generators be the Lie algebra of the correspon…

The integrable map corresponding to the linear equation, respectively the nonlinear equation, is denoted by … . A nonlocal diffeomorphism is a diffeomorphism whose action is nonloc…

Let a QP differential system be given, and consider the multiplicative and additive discretizations … के and … where each $\varphi_i$ is differentiable. Commutativity conjecture. F…