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**mathaholic****Member**- From: Earth
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34661

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**bobbym****Administrator**- From: Bumpkinland
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80^2 + 102^2 + 134^2 = 34760

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**mathaholic****Member**- From: Earth
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34869

Mathaholic | 17th most active poster | 681st most recent person to join MIFF | Person | rrr's classmate

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**bobbym****Administrator**- From: Bumpkinland
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92^2 + 98^2 + 130^2 = 34968

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

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**mathaholic****Member**- From: Earth
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35067

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**bobbym****Administrator**- From: Bumpkinland
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94^2 + 101^2 + 127^2 = 35166

**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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**mathaholic****Member**- From: Earth
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35265

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**bobbym****Administrator**- From: Bumpkinland
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92^2 + 100^2 + 130^2 = 35364

**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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**mathaholic****Member**- From: Earth
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35463

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**bobbym****Administrator**- From: Bumpkinland
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92^2 + 97^2 + 133^2 = 35562

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

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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'

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**bobbym****Administrator**- From: Bumpkinland
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By a program that does them for me.

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

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

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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'

'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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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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.**

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

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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'

'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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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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.**

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

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36255

But ..... The proof?

'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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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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.**

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

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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'

'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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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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.**

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

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**mathaholic****Member**- From: Earth
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36651

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**bobbym****Administrator**- From: Bumpkinland
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109^2 + 110^2 + 113^2 = 36750

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

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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'

'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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 97,222

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.**

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

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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'

'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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