Waste less time on Facebook — follow Brilliant.
×

Interesting :)

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

Note by Victor Loh
3 years, 6 months ago

No vote yet
1 vote

  Easy Math Editor

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears 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

Sort by:

Top Newest

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 - 3 years, 6 months ago

Log in to reply

Oh it's one of my school problems :D

Victor Loh - 3 years, 6 months ago

Log in to reply

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

Krishna Ar - 3 years, 6 months ago

Log in to reply

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

Victor Loh - 3 years, 6 months ago

Log in to reply

@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 - 3 years, 6 months ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...