Interesting :)

Show that $3^{2008}+4^{2009}$ can be written as a product of two positive integers each of which is larger than $2009^{182}$ .

Easy Math Editor

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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}`	$\boxed{123}$

Comments

Sophie Germain. Sorry that I didnt post a proof but I guess its easy to proceed once you write it as $a^{4}+4b^{4}$ By the way, I am curious- Where did you get this from @Victor Loh ? This same problem appeared in TNMO-2009!! Whoa!!! I am supercurious!!!

Krishna Ar - 6 years, 10 months ago

Oh it's one of my school problems :D

Victor Loh - 6 years, 10 months ago

How come a TNMO problem is a Raffles'Problem? Do they teach you such advanced math at 12? I'm amazed.

Krishna Ar - 6 years, 10 months ago

@Krishna Ar – I'm in a special pull-out class where we learn harder math than the mainstream students :)

Victor Loh - 6 years, 10 months ago

@Victor Loh – Lucky~!!!! You!!!. I sneak in the higher math books through my boring school classes and the next few days are gonna have more of'em :O :P

Krishna Ar - 6 years, 10 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}`	$\boxed{123}$