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#51 2014-05-10 14:49:41

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 22,021
Website

Re: Number Theory

What are the philosophers paid for?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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#52 2014-05-10 14:54:22

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 97,302

Re: Number Theory

For one thing they can head over to a university and find teaching jobs or author a book.

5251.gif


In mathematics, you don't understand things. You just get used to them.

If it ain't broke, fix it until it is.

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#53 2014-05-10 16:42:25

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 22,021
Website

Re: Number Theory

It looks like they are teaching each other expressions.


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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#54 2014-05-10 20:01:53

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 97,302

Re: Number Theory

They are both going Hmmm.


In mathematics, you don't understand things. You just get used to them.

If it ain't broke, fix it until it is.

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#55 2014-05-11 01:41:22

zetafunc.
Guest

Re: Number Theory

bob bundy wrote:

To extract a contradiction argument you would have to assume that x + y ≠  88 and show this leads to a contradiction.  Since many other values (other than 88) are possible, I think you'd have a tough time with this.

Bob

It might be doable -- I haven't tried via contradiction, although I'd assume you'd start with x + y < 88 and find bounds for a + b + ab that don't include 2020, then do something similar for the case x + y > 88. The AM-GM inequality might help for this due to the ab term. However, the problem seems engineered to make use of the factorisation (a + 1)(b + 1) - 1 = a + b + ab.

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