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.

Easy Math Editor

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Comments

Okay, here is the solution.

Kartik Sharma - 4 years, 5 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$