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**mathaholic****Member**- From: Juliania
- Registered: 2012-11-29
- Posts: 2,842
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34661

"Double the fun, double the thrill, double the coolness" - Julianthewiki

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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80^2 + 102^2 + 134^2 = 34760

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**mathaholic****Member**- From: Juliania
- Registered: 2012-11-29
- Posts: 2,842
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34869

"Double the fun, double the thrill, double the coolness" - Julianthewiki

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,362

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

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**mathaholic****Member**- From: Juliania
- Registered: 2012-11-29
- Posts: 2,842
- Website

35067

"Double the fun, double the thrill, double the coolness" - Julianthewiki

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,362

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

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**mathaholic****Member**- From: Juliania
- Registered: 2012-11-29
- Posts: 2,842
- Website

35265

"Double the fun, double the thrill, double the coolness" - Julianthewiki

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,362

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

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**mathaholic****Member**- From: Juliania
- Registered: 2012-11-29
- Posts: 2,842
- Website

35463

"Double the fun, double the thrill, double the coolness" - Julianthewiki

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,362

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

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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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'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,362

By a program that does them for me.

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

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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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'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,362

Mathematica yes.

Sum of squares? Yes there is a proof.

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

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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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'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,362

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

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

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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36255

But ..... The proof?

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

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,362

The proof? What proof are we talking about?

2 x 107^2 + 116^2 = 36354

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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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'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,362

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

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**mathaholic****Member**- From: Juliania
- Registered: 2012-11-29
- Posts: 2,842
- Website

36651

"Double the fun, double the thrill, double the coolness" - Julianthewiki

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,362

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

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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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'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,362

Hi;

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

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

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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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'

'Humanity is still kept intact. It remains within.' -Alokananda

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