5 problems

Conjecture 3. The system $S$ has a solution $(x_1,\ldots,x_n)\in (G\cap\mathbb Q)^n$ such that

Nonvanishing conjecture. The polynomial $P_N$ satisfies

Let $N$ be an even positive integer, and consider the associated $N$-periodic dressing-chain system and its shift operators. A first-order polynomial solution means one of the firs…

An exponential Diophantine equation over $\mathbb Q$ is an equation built using variables, rational constants, arithmetic operations, and exponentiation with nonnegative base and e…

Completeness conjecture. The construction includes all possible rational solutions to the system.