Activity for Lisanne
| Type | On... | Excerpt | Status | Date |
|---|---|---|---|---|
| Comment | Post #288505 |
https://oeis.org/A331399 gives solutions to the Pell equation with p and q prime. It only lists 5 terms, so maybe those are all? (more) |
— | 8 months ago |
| Edit | Post #291395 | Initial revision | — | 8 months ago |
| Answer | — |
A: Seeking a theorem about lattices Neukirch - Algebraic Number Theory proposition 4.2 states that a subgroup of $\mathbb{R}^n$ is discrete if and only if it is a lattice. A lattice has a linearly independent basis by definition, so it has rank at most $n$. (more) |
— | 8 months ago |
| Edit | Post #291394 | Initial revision | — | 8 months ago |
| Answer | — |
A: How to find perfect squares such that their base 9 representation is all 1s? First I plug in $k = 1,...,4$ and only find $k=1$ as a solution. Hence I conjecture that there are not solutions apart from $k = 1$ Before we prove this we should recall the geometric series formula $$\sum{i = 0}^k 9^i = \frac{9^k - 1}{9 - 1}.$$ (prove this via induction or using polynomials) ... (more) |
— | 8 months ago |