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We are interested in small integer solutions to the Pell equation: $$x^2-a^3 y^2=\pm 1 \qquad (1)$$ Where in $\pm 1$ you can chose either sign. $(x^2,a^3 y^2)$ are consecutive powerful numbers. $abc$ ...

Let $f(n)$ be an arbitrary function such that $f(n)\in\mathbb{Z}$. Let $$ F(x)=\sum\limits_{m\geqslant 0}f(m)x^m $$ Define the operator $\operatorname{SR}$, which is associated with the series ...

I'm looking for some unpublished notes called "Eta Lore," which are apparently related to a talk Douglas Hofstadter first gave at the Stanford Math Club in 1963. I know these notes exist because they'...