# Limiting the modulo products

$\displaystyle \lim_{n \to \infty} {\left(\dfrac{\displaystyle \prod_{\substack{m \left \lfloor n/t\right \rfloor \le k \le mn \\ k\mod{m} \equiv p}} k}{\displaystyle \prod_{\substack{m \left \lfloor n/t\right \rfloor \le k \le mn \\ k\mod{m} \equiv q}} k }\right)} = t^{(p-q)/m}$

Try to prove this. Observe what all it is trying to express.

Note by Kartik Sharma
1 year, 6 months ago

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Okay, here is the solution.

- 1 year, 6 months ago