Tessellate S.T.E.M.S. (2019) - Mathematics - School - Set 1 - Subjective Problem 1

Consider all positive integers $a,b,n$ such that $a!b!|n!$ . Prove there exists a constant $c$ such that for all such $a,b,n$ we have $a+b<n+clog_{10}(n)$ . (The constant $c$ works for all positive integers $a, b, n$ having the said property.)

This problem is a part of Tessellate S.T.E.M.S. (2019)

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`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`	$\sin \theta$
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Comments

Are these practice problems for the examination?

Abha Vishwakarma - 2 years, 8 months ago

Apologies for the late reply, but yes they are problems meant to give you a rough idea of the difficulty level of the examination. The problems may not resemble the ones asked in the actual exam, and the exact format of the exam will be as you will see in the Sample Problems section.

Cheers. Tessellate Stems Math Committee.

Tessellate S.T.E.M.S. Mathematics - 2 years, 8 months ago

Where can I look for the solution?

Anu Radha - 2 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}`	$\boxed{123}$