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**mathaholic****Member**- From: idk
- Registered: 2012-11-29
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34661

It's summer.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 93,618

80^2 + 102^2 + 134^2 = 34760

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

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**mathaholic****Member**- From: idk
- Registered: 2012-11-29
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34869

It's summer.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 93,618

92^2 + 98^2 + 130^2 = 34968

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

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**mathaholic****Member**- From: idk
- Registered: 2012-11-29
- Posts: 2,909
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35067

It's summer.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 93,618

94^2 + 101^2 + 127^2 = 35166

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

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**mathaholic****Member**- From: idk
- Registered: 2012-11-29
- Posts: 2,909
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35265

It's summer.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 93,618

92^2 + 100^2 + 130^2 = 35364

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

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**mathaholic****Member**- From: idk
- Registered: 2012-11-29
- Posts: 2,909
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35463

It's summer.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 93,618

92^2 + 97^2 + 133^2 = 35562

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

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35661

How are you getting those expansions?

'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'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 93,618

By a program that does them for me.

52^2 + 116^2 + 140^2 = 35760

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

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35859

Mathematica?

Do you have a proof that this can be done as for all numbers?

'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'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 93,618

Mathematica yes.

Sum of squares? Yes there is a proof.

74^2 + 91^2 + 149^2 = 35958

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

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36057

Will you please post it?

'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'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 93,618

91^2 + 93^2 + 95^2 + 101^2 = 36156

```
PowersRepresentations[36156, 4, 2]//Last
yields:{91,93,95,101}
```

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

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36255

But ..... The proof?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 93,618

The proof? What proof are we talking about?

2 x 107^2 + 116^2 = 36354

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

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36453

bobbym wrote:

Sum of squares? Yes there is a proof

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 93,618

I think it was Legendre who proved that 4 squares were enough for any number. The proof requires quarternions.

94^2 + 104^2 + 130^2 = 36552

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

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**mathaholic****Member**- From: idk
- Registered: 2012-11-29
- Posts: 2,909
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36651

It's summer.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 93,618

109^2 + 110^2 + 113^2 = 36750

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

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36849

Is it like a complex hyperspace where both the axes are complex?

If ij =k then how can ji = -k, that makes sense?

*Last edited by Agnishom (2013-04-07 14:16:17)*

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 93,618

Hi;

That I do not know because I know nothing about complex hyperspace.

92^2 + 110^2 + 128^2 = 36948

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

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37047

What about the proof, then?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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