All Questions

Assume that $J$ is the interval $(-\pi,\pi]$. For $k=1,\ldots,2n$, suppose that $\lambda_k$s are real functions on $J$ with $|\lambda_k|=1$, meaning that $\lambda_k(t)$ is either $-1$ or $1$ where $t\...

I have the self-referencing recurrence relation $$ d(0) = 0 $$ $$ d(1) = a $$ $$ d(n+1) = d(n) + a*e^{-(\frac{d(n)-n*c}{b})^4} $$ Written as a sum: $$ d(N) = a*\sum_{n=0}^{N}e^{-(\frac{d(n)-n*c}{b})^...

Given a non-negative number n, what is the best approach to find the most compact representation for n in terms of sums of powers, such that the bases and the exponents can't surpass a given value (...

I want to ask about decidability of exponential Diophantine equation: $z_12^{\eta_1} + \ldots + z_n2^{\eta_n} = z$, where $z_i,\eta_i,z \in \mathbb{Z}$, and $\eta_i$ - are variables. Can we find ...