All Questions

WillJagy answered a linear relation question on Pythagorean Triples in Small linear relations between primitive Pythagorean triples $\mathsf I$. Now let $a^2+b^2=c^2$ be a primitive Pythagorean ...

The easier Waring problem asks for the least number $v=v(k)$ such that every every integer is a sum of $v$ $k$'th powers with signs, i.e. every $n\in \mathbb{N}$ is of the form $$n=x_1^k\pm x_2^k\pm\...

Let $k$ be a positive integer. Note that $a/b=ab^{k-1}/b^k$ for any integers $a$ and $b>0$. If every $n\in\mathbb N=\{0,1,2,\ldots\}$ can be written as $x_1^k+\cdots+x_{s}^k$ with $x_1,\ldots,x_s\...

This is related to cryptography and this question and another question. In short, we are asking about decomposing multivariate polynomial as sum of perfect powers of linear polynomials. Working over $\...

Let $N(h)$ be the number of solutions of the following linear diophantine equation: \begin{equation} x_1 + 2x_2 + 3x_3 + \dots + (h-1)x_{h-1} = 6h-6; \end{equation} where $h\geq 2$ and solution means ...