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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 92,978

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.**

**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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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'

'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: 92,978

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.**

**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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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'

'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: 92,978

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 That model is obsolete.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.**

**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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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'

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

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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'

'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: 92,978

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.

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

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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'

'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: 92,978

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

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

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No, 20

'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: 92,978

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?

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

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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'

'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: 92,978

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.

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

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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'

'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: 92,978

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.

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

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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'

'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: 92,978

Not in Mathematica!

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

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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'

'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: 92,978

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

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

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