# Tagged Questions

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### Find the generating function for a series , given a recurrence relation

I am solving a problem on an Online Judge. The problems solution boils down to find the solutions to the following recurrence relation: ...
155 views

### Coefficients in expansion of $(\sqrt[3]{2} - 1)^m$

In trying to solve $a^3 - 2b^3 = 1$ over the integers I came across the need to answer the question: when does $(1+ \sqrt[3]{2} + \sqrt[3]{2}^2)^n$ have no $\sqrt[3]{2}^2$ term in it's expansion (in ...
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### Proof that $x^2 - 2y^2 = -1$ has a recurring solution for $x$

I read here about the following variation on Pell's equation: $$x^2 - 2y^2 = -1.$$ According to Dario Alpern's solver, the equation has infinite integer ...
### Alternative solutions to $n^2+n = k^2+k + 2kn$
Consider this equation: $n^2+n = k^2+k + 2kn$ I want to find the set of non-negative integer n,k that satisfies the equation. I tried to write $n$ as $k$ by solving the equation with $n$ as root ...