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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi,

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,243

Hi gAr;

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi bobbym,

It's actually a putnam question. The original question was a continued fraction, and it needs the answer to be in that form.

*Last edited by gAr (2011-04-18 18:15:43)*

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,243

Hi gAr;

That is how I solved it. One way was with a PSLQ, the other was with a continued fraction. Please hold on, I am swamped. I will write up what I did.

Putnam questions are really hard, so do not be suprised if I am wrong.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Okay.

No hurry.

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,243

First, did I get close to the right answer or do I need to more work?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Your answer is correct.

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,243

Hi gAr;

This is not rigorous enough for a putnam problem but I did not know that when you posted it.

The cf for

You can replace the infinite portion of the cf with y - 2.

Now just solve for y.

The simplification was done by the continued fraction for us. The only weak part is that you need to prove that is the cf of your irrational number.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi bobbym,

The only weak part is that you need to prove that is the cf of your irrational number.

That's the only part I need to know!

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,243

Hi gAr;

There are recurrences to get the continued fraction from a quadratic surd. You could raise the LHS up the 8th power and work with that one. It will produce a repeating cf and according to Legendre it will do it in 10 or less iterations.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi bobbym,

Okay. I'll check.

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi,

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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