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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,676

He proved the 3 squares theorem.

But the point is any natural number can be represented by 4 squares or less. Does that spark your synapses? can you now solve the problem?

**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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I already knew that theorem. Why?

'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: 86,676

Try to think like that computational guy we know. What would he do with that?

**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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Please look at the link in post 38

'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: 86,676

I remember your program and your level of understanding at that time. You are no longer that Agnishom, you are this Agnishom. That model is obsolete. You asked how to do it in M. I ask again, what does the previous posts make you think of?

**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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I ask again, what does the previous posts make you think of?

I understood nothing of the algorithm then, nor do I now. I just translated it from human language to a programming language.

'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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This problem recently came up on Brilliant https://brilliant.org/discussions/threa … e-theorem/

'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: 86,676

So let's look at an easier problem. Supposing you want to break a number into 8 squares with M. How can you do it quickly? You know M can always get 4 squares for any number and darn quickly too. Why? Because Lagrange, Legendre, Gauss, Cayley and others say so.

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

Combinatorics is Algebra and Algebra is Combinatorics.

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You know M can always get 4 squares for any number and darn quickly too. Why?

No, It is taking forever for my 10 digit number.

'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: 86,676

You are trying to get them all with that command. We are discussing how to get one answer.

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

Combinatorics is Algebra and Algebra is Combinatorics.

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No, 20

'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: 86,676

But if you can not do 8, how can you do 20? We solve a bigger problem by breaking it up into many smaller ones. Each which is solvable. If you know how to do 4 then how do you do 8?

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

Combinatorics is Algebra and Algebra is Combinatorics.

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Please tell me what is the problem that I must solve now precisely

'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: 86,676

Okay, you do not know the beginning solution so please open up another thread in Computer Math and ask the question clearly. Remember, others will be seeing it.

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

Combinatorics is Algebra and Algebra is Combinatorics.

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you do not know the beginning solution

Please tell me the question first.

'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: 86,676

You want to know how to represent a 10 digit number as a sum of 20 squares. So post that as your question.

Right now you do not know how to even get it in 4 squares.

We will discuss the answer over there.

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

Combinatorics is Algebra and Algebra is Combinatorics.

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You want to know how to represent a 10 digit number as a sum of 20 squares.

Ofcourse not!

I want 20 ways to represent a 10 digit number as a sum of 4 squares.

Right now you do not know how to even get it in 4 squares.

Ofcourse I do!

'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: 86,676

Not in Mathematica!

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

Combinatorics is Algebra and Algebra is Combinatorics.

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I could translate that to M code but it would be a poor idea.

'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: 86,676

Very poor. Generally, M is for functional or rule based programming. Procedural code is always slower.

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

Combinatorics is Algebra and Algebra is Combinatorics.

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