Questions tagged [modular-arithmetic]
The modular-arithmetic tag has no usage guidance.
3
questions
19
votes
3
answers
977
views
Conjecture $ \sum _{i=1}^{n-1}\lfloor \frac{i^2}{n}\rfloor \ge \frac{\left(n-1\right)\left(n-2\right)}3$ where $n\in\mathbb N^*$
This is a question I also asked on MSE . If it is frowned upon to ask the same question on both threads, you can vote to close this thread.
Let $n \in \mathbb {N^*}$ and $$S_n = \sum_{k=1}^{n-1} (k^2 \...
- 1,503
2
votes
1
answer
211
views
An arithmetic problem involving a system of equations
Fix a positive integer $r$. Describe the solutions to the system of equations given by:
$$\begin{equation}\sum_{1\leq i\leq r}X_i^2\equiv0\pmod{X_k}(1\leq k\leq r)\end{equation}$$
Example: In the case ...
- 917
0
votes
0
answers
23
views
Min-norm solution of over-specified linear system of $p$-adic equations
(Note: this is cross-posted with https://math.stackexchange.com/questions/4747805/min-norm-solution-of-over-specified-linear-system-of-p-adic-equations. I am posting it here as I got no answer after 1 ...
- 1