You are Here: Home >< Maths

# The Proof is Trivial! Watch

1. (Original post by Lord of the Flies)
Maybe one day, you'll agree on the beauty of this as well...

When an integer, it is a perfect square.

Spoiler:
Show

(by the way I am not posting this as a problem for the thread)
Took me a while to remember that incident
2. (Original post by Lord of the Flies)
It is a */**, but a difficult one.

(the joke was that it requires a mathematical argument which I love and which bananarama despises - I'll let you figure out what it is from the picture)

Wasn't L'art's the gamma function, and yours was proof by infinite descent?
3. Has anyone got a solution for 192?
4. (Original post by ukdragon37)
Spoiler:
Show
Unfortunately those stairs are very unlikely to be long enough for the analogy to be apt.
Yeah but know what else isn't long enough? Your dissertation.

(Original post by Zakee)
Wasn't L'art's the gamma function, and yours was proof by infinite descent?
That sounds about right. Things have changed a bit though - I'm hitting on her twin sister now.
5. (Original post by Lord of the Flies)
Yeah but know what else isn't long enough? Your dissertation.

That sounds about right. Things have changed a bit though - I'm hitting on her twin sister now.

Who? Suzy? . Way to go, alpha-male. Or should I say, beta-male.
6. (Original post by Lord of the Flies)
Yeah but know what else isn't long enough? Your dissertation.
No worries, I'm making good progress

Spoiler:
Show
7. (Original post by ukdragon37)
No worries, I'm making good progress

Spoiler:
Show
You definitely need iced coffee, not that coffee, in this weather ;P
8. (Original post by bananarama2)
You definitely need iced coffee, not that coffee, in this weather ;P
There's good weather outside? *checks* So there is.
9. (Original post by ukdragon37)
There's good weather outside? *checks* So there is.
10. Solution 185

Clearly, is strictly increasing function; we set . We note that and
As over the whole real line, we can introduce , which is obviously increasing; .
Now, . Suppose . Thus or , for gives and hence for all .
Therefore, .

Solution 186

Imprimis, we notice that for each , there exists such that .
Secondly, is injective. Otherwise, for .
The equality is impossible. If it were true, then we would have , which is clearly not true.
Let , . The inequality holds true, for does not have any fixed points!
Hence, or . As , we have . It is obvious that , and thus . Following this path, we arrive at , which is a contradiction.

Solution 192

Suppose . We can also suppose that . Consider ; let, . Then, over . Moreover, there exists such that , which implies that decreases from zero to - contradiction.
Hence .
Suppose . On the one hand, by the definition of . On the other hand, however, we have , from the condition , which is a contradiction.

I suppose that is continuous at and .

Solution 195

Let be an arithmetic progression with non-zero common difference. Then, which has infinitely many solutions in positive integers. We derive this result from a more general theorem about ternary forms.

Solution 196

The elliptic curve coincides with the modular curve . Hence . Therefore, are the only -rational points on the curve, and these points correspond to trivial solutions.

There are not enough number theory problems...

Problem 202**

Find all polynomials such that, for all , there exists at least one integer such that .

Problem 203**

For any positive integer set . Find all such that is irreducible over .

Problem 204**

Let be a prime number, and be arbitrary integers. Let be the number of different reminders of , and modulo .
Prove that implies and - .
...
I must say, I've never seen the word imprimis used before. It does add a certain credibility to your solution though I might try to sneak that word into my future solutions too!
12. (Original post by such)
I must say, I've never seen the word imprimis used before. It does add a certain credibility to your solution though I might try to sneak that word into my future solutions too!
Lovely scrabble word, I should try and use it in the future.
13. (Original post by Lord of the Flies)
Maybe one day, you'll agree on the beauty of this as well...

When an integer, it is a perfect square.

Spoiler:
Show

(by the way I am not posting this as a problem for the thread)
Prove it (it's supposed to be the hardest ever IMO question set, but I don't think that's true).
14. (Original post by shamika)
Spoiler:
Show
Prove it (it's supposed to be the hardest ever IMO question set, but I don't think that's true).
The hardest IMO?! Vieta jumping kills it in three lines. For those who know not this method - click.

The difficulty of a given question is a relative concept. However, I would vote for IMO 2002 Problem 6.
In my view, the most difficult problem which has ever been proposed for IMO is Problem 6 Algebra IMO SL 2003.

(Original post by such)
Spoiler:
Show
I must say, I've never seen the word imprimis used before. It does add a certain credibility to your solution though I might try to sneak that word into my future solutions too!
Edgar Allan Poe is an influential writer, you know.
15. (Original post by shamika)
Prove it (it's supposed to be the hardest ever IMO question set, but I don't think that's true).

I tried to, today. (I've heard of Vieta Jumping but never bothered to look at it). Safe to say, my attempts have been futile. I've got somewhere, but all that is similar to a real solution is that I've used mathematics to yield more mathematics.

Edit: Looking at Vieta Jumping now, Mlad was right. Wow. That's so much simpler, haha.
16. (Original post by Zakee)
I tried to, today. (I've heard of Vieta Jumping but never bothered to look at it). Safe to say, my attempts have been futile. I've got somewhere, but all that is similar to a real solution is that I've used mathematics to yield more mathematics.

Edit: Looking at Vieta Jumping now, Mlad was right. Wow. That's so much simpler, haha.
This is the same problem I showed you earlier.

17. (Original post by MW24595)
This is the same problem I showed you earlier.

Mhm, I do. The students and the Australian committee. . Don't worry, Go buy Chai (Ngo Bao Chu) will meet his match. (I'm changing my name to Go buy Lipton).
18. Just for anyone who's doing any late night Mathematics/Studying/Procrastination (the most likely option), here's a small meme to cheer you up:

19. (Original post by such)
I must say, I've never seen the word imprimis used before. It does add a certain credibility to your solution though I might try to sneak that word into my future solutions too!
Edgar Allan Poe is an influential writer, you know.
Personally I like "ansatz".
20. (Original post by Zakee)
Just for anyone who's doing any late night Mathematics/Studying/Procrastination (the most likely option), here's a small meme to cheer you up:

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: December 11, 2017
Today on TSR

### What is the latest you've left an assignment

And actually passed?

### Simply having a wonderful Christmas time...

Discussions on TSR

• Latest
• ## See more of what you like on The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

• Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams

## Groups associated with this forum:

View associated groups
Discussions on TSR

• Latest
• ## See more of what you like on The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

• The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.