You are Here: Home >< Maths

The Proof is Trivial! Watch

Problem 257 */**

How many subsets of are there such that the sum of the smallest and largest element is ?
Solution # 257

Spoiler:
Show

2^8+2^6...2^2 +2^0= 1(4^5-1)/3= 341
2. (Original post by Blutooth)
...
Do you want to put "Solution #" on top.
Do you want to put "Solution #" on top.
no problem
4. (Original post by theterminator)
http://theproofistrivial.com/ - What? :P
LOL Blatantly gonna start sending people that link hahahahahaha

(Original post by und)
x
What did you call it "The Proof is Trivial!" btw?
5. (Original post by Jkn)
What did you call it "The Proof is Trivial!" btw?
The name of this thread comes from that link (it used to be in my signature)
6. (Original post by Lord of the Flies)
Here is a truly sensuous result.

Problem 192*

is a twice-differentiable function with continuous derivatives, and satisfies the following conditions over

Show that
Has anybody got a solution they'd like to post?
7. (Original post by bananarama2)
Why does the first one seem so familiar?
I remember it, too. I think it was the first problem I solved which you guys (current 6th formers) were interested in.
8. (Original post by Lord of the Flies)
The name of this thread comes from that link (it used to be in my signature)
You've got a good taste in music BTW
9. (Original post by Felix Felicis)
Spoiler:
Show
Problem from ages ago :L

Solution 168 (2)

This was a slog but the Beta and Gamma functions are sexy

Let

Now, consider

Differentiating under the integral sign, we get:

which is x8 of the desired integral for a, b = 0

Furthermore, we have:

stuff

Using the result that we get that:

where is the Euler-Mascheroni constant

and that

Using the definition that

we get (sum reduces to Basel problem)
Gorgeous.
Shamelessly so.
10. (Original post by theterminator)
Has anybody got a solution they'd like to post?
There's a link to the solution in the OP
11. (Original post by Felix Felicis)
There's a link to the solution in the OP
I see. Thank you. I only just realised that there was a second post.. :P
12. Is there a function which takes prime numbers as values on all positive integers?

Spoiler:
Show

I am looking for a general comment.
Is there a function which takes prime numbers as values on all positive integers?

Spoiler:
Show

I am looking for a general comment.
Could you elaborate a bit more on the conditions? I can think of periodic functions where every integer input of x gives prime numbers but only a specific subset. However, I'm not sure if this is quite what you're asking.

(E.g. gives a prime output for every integer input, but only 2 specific ones.)
14. (Original post by DJMayes)
However, I'm not sure if this is quite what you're asking.
What you gave is a good example. I am looking for a function that assumes infinitely many primes as values.
Is there a function which takes prime numbers as values on all positive integers?

Spoiler:
Show

I am looking for a general comment.
Surely there is no known function which gives different primes for each integer. If I find it do I get a millions pounds (and a job which GCHQ)?
16. (Original post by bananarama2)
Surely there is no known function which gives different primes for each integer. If I find it do I get a millions pounds (and a job which GCHQ)?
I claim there exists a constant such that is a prime for all .
Is there a function which takes prime numbers as values on all positive integers?

Spoiler:
Show

I am looking for a general comment.
5(n2n) + 1
I claim there exists a constant such that is a prime for all .

(Original post by MAyman12)
5(n2n) + 1
Interesting, it appears I'm very much mistaken. Pfft all this maths nonsense
Is there a function which takes prime numbers as values on all positive integers?

Spoiler:
Show

I am looking for a general comment.
Yes,

f(x)= x if x is prime, 0 otherwise

will work.
20. (Original post by bananarama2)
Interesting, it appears I'm very much mistaken. Pfft all this maths nonsense
I just think Mills' constant is under-appreciated and decided to promote it. Actually, there are uncountably many such .

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: January 5, 2018
Today on TSR

Should I ask for his number?

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

Chat with other maths applicants

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