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#76 2013-04-15 01:06:12

bobbym
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Re: Four Square

That expression gets the second square before the first. We could iterate again and get the third, fourth or fifth.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#77 2013-04-21 13:59:34

Agnishom
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Re: Four Square

I just coded it and it worked!


'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'
'Who are you to judge everything?' -Alokananda

#78 2013-04-21 16:41:49

bobbym
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Re: Four Square

Hi Agnishom;

Which did you code?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#79 2013-04-21 17:49:47

Agnishom
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Re: Four Square

This: http://www.alpertron.com.ar/4SQUARES.HTM

Wait, something's wrong: it can't decompose numbers like 130, 520, 2080, 8320, 33280, 133120 and I can't understand 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'
'Who are you to judge everything?' -Alokananda

#80 2013-04-21 21:34:25

bobbym
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Re: Four Square

All those numbers are divisible by 130. Can it do 16?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#81 2013-04-21 22:31:49

Agnishom
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Re: Four Square

Yes.

(All numbers between them and less than them can be done)


'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'
'Who are you to judge everything?' -Alokananda

#82 2013-04-21 22:47:18

bobbym
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Re: Four Square

There are



for 130. Maybe his algorithm is not correct.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#83 2013-04-21 22:52:39

Agnishom
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Re: Four Square

What they simply say:
💫Express the original number in the form n = 4^r*s where s is not multiple of 4.
💫💫Compute the square root of s. If this number squared equals s, the original number is a perfect square, so skip the following two steps.
💫💫💫 If s < 7 (mod 8) the number can be expressed as a sum of three squares. Subtract a square and check whether the result has the form 2^m (4k+1) where m is a non-negative integer. If not, select another square and repeat. Finally check if the number 4k+1 is prime. If not, select another square and repeat. The resulting difference, 2^m (4k+1), can be expressed as a sum of two squares as explained in 🌟. In the sequence of squares, the first attempt should be zero in order to minimize the number of summands in the decomposition.
💫💫💫💫Otherwise, the number must be expressed as a sum of four squares. Subtract two perfect squares from s such that the difference has the form 2^m (4k+1) and proceed as in the previous step.
💫💫💫💫💫At this moment s = a^2 + b^2 + c^2 + d^2, where some variables can be equal to zero. Multiply by 4^r to get n = (2^r a)^2 + (2^r b)^2 + (2^r c)^2 + (2^r d)^2.

🌟This one, I don't get but I use the greedy algorithm

Last edited by Agnishom (2013-04-21 22:54:03)


'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'
'Who are you to judge everything?' -Alokananda

#84 2013-04-21 23:03:43

bobbym
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Re: Four Square

Did you try his applet at the bottom and see if it works on 130?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#85 2013-04-21 23:08:33

Agnishom
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Re: Four Square

Let me do that now.

BTW Can you see this: 🌟💫


'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'
'Who are you to judge everything?' -Alokananda

#86 2013-04-21 23:09:03

bobbym
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Re: Four Square

Hi;

No, I can not.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#87 2013-04-21 23:14:09

Agnishom
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Re: Four Square

Oh! Then #84 won't make sense to you.

Yes, it can decompose 130 and that is sad


'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'
'Who are you to judge everything?' -Alokananda

#88 2013-04-21 23:19:02

bobbym
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Re: Four Square

How did you express 130 in the form of 4^r * s?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#89 2013-04-21 23:32:46

Agnishom
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Re: Four Square

Repeated division by 4.

The problem is here I guess:

Subtract a square and check whether the result has the form 2^m (4k+1) where m is a non-negative integer.


'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'
'Who are you to judge everything?' -Alokananda

#90 2013-04-21 23:50:23

bobbym
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Re: Four Square

Hi;

There is no form 4^r *s = 130

Also, 130 is representable as the sum of 2 squares.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#91 2013-04-21 23:52:18

Agnishom
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Re: Four Square

(4^0)*(130) = 130


'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'
'Who are you to judge everything?' -Alokananda

#92 2013-04-22 00:02:08

bobbym
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Re: Four Square

What did you now get for this step?

2^m (4k+1)


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#93 2013-04-22 00:11:52

Agnishom
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Re: Four Square

That is the problem, I can't do it. 4k + 1 isn't being a prime


'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'
'Who are you to judge everything?' -Alokananda

#94 2013-04-22 00:13:59

bobbym
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Re: Four Square

When you ran his applet, what was his answer for 130?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#95 2013-04-22 02:13:44

Agnishom
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Re: Four Square

7**2 + 9**2


'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'
'Who are you to judge everything?' -Alokananda

#96 2013-04-22 02:40:02

bobbym
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Re: Four Square

Maybe I am missing something but how do you know what square to subtract?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#97 2013-04-22 03:15:01

Agnishom
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Re: Four Square

I am starting from 0, then 1 then 4 then 9 then 16 and so on..

Last edited by Agnishom (2013-04-22 03:15:28)


'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'
'Who are you to judge everything?' -Alokananda

#98 2013-04-22 03:27:30

bobbym
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Re: Four Square

Let me look at it for awhile.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#99 2013-04-22 03:40:28

Agnishom
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Re: Four Square

look for what?


'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'
'Who are you to judge everything?' -Alokananda

#100 2013-04-22 03:43:16

Agnishom
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Re: Four Square

See this one: http://agnishom.tumblr.com/post/48531450618/splitting-an-integer-into-four-squares


'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'
'Who are you to judge everything?' -Alokananda

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