Mathematics

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No Flag Jaeger
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Re: Mathematics

Post by Jaeger »

Anyone have any cool problems they would like to share? I just did a pretty cool one, the proof is easy if you know how to start it but finding the right direction to start in may or may not take some time. I saw this problem before a few years ago and I had to look up the solution, but I tried solving it now again and found another way to do it:

If S can be expressed as the sum of two squares, show that 2S can be expressed as the sum of two squares, and show that 5S can be expressed as the sum of two squares (integers only ofc)
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Re: Mathematics

Post by Jaeger »

@Jerom @Garja hy isn't this thread showing in active threads? :(
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Re: Mathematics

Post by Garja »

It's off-topic section. Site admin changed that recently.
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Re: Mathematics

Post by Jaeger »

Garja wrote:It's off-topic section. Site admin changed that recently.

Site admin as in divinefire? Is he still around? I haven't seen him post in months.
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Re: Mathematics

Post by BrookG »

ovi12 wrote:Anyone have any cool problems they would like to share? I just did a pretty cool one, the proof is easy if you know how to start it but finding the right direction to start in may or may not take some time. I saw this problem before a few years ago and I had to look up the solution, but I tried solving it now again and found another way to do it:

If S is the sum of two positive integers, show that 2S and 5S are the sum of 2 positive integers as well.

I think it's obvious they are sum of 2 positive integers. :hmm: Maybe you mean something like odd or even?
Correlation doesn't mean causation.
http://www.tylervigen.com/spurious-correlations

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No Flag Jaeger
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Re: Mathematics

Post by Jaeger »

BrookG wrote:
ovi12 wrote:Anyone have any cool problems they would like to share? I just did a pretty cool one, the proof is easy if you know how to start it but finding the right direction to start in may or may not take some time. I saw this problem before a few years ago and I had to look up the solution, but I tried solving it now again and found another way to do it:

If S is the sum of two positive integers, show that 2S and 5S are the sum of 2 positive integers as well.

I think it's obvious they are sum of 2 positive integers. :hmm: Maybe you mean something like odd or even?

Lol wtf was i writing i meant squares. If S can be expressed as the sum of two squares, show that 2S can be expressed as the sum of two squares, and show that 5S can be expressed as the sum of two squares (integers only ofc)
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No Flag Jaeger
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Re: Mathematics

Post by Jaeger »

I think i meant to write "perfect square" but i wrote positive integer instead
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Re: Mathematics

Post by iNcog »

-- deleted post --

Reason: on request (off-topic bulk delete)
YouTube: https://www.youtube.com/incog_aoe
Garja wrote:
20 Mar 2020, 21:46
I just hope DE is not going to implement all of the EP changes. Right now it is a big clusterfuck.
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Re: Mathematics

Post by Jaeger »

iNcog wrote:
ovi12 wrote:
Garja wrote:It's off-topic section. Site admin changed that recently.

Site admin as in divinefire? Is he still around? I haven't seen him post in months.


it's buckethead

not a bad thing either, can't have new people getting in on all those off topic shitposts lol

What happened to divine? Did he get fired?
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Re: Mathematics

Post by momuuu »

Divine is experiencing real life.
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Re: Mathematics

Post by iNcog »

-- deleted post --

Reason: on request (off-topic bulk delete)
YouTube: https://www.youtube.com/incog_aoe
Garja wrote:
20 Mar 2020, 21:46
I just hope DE is not going to implement all of the EP changes. Right now it is a big clusterfuck.
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Re: Mathematics

Post by iNcog »

-- deleted post --

Reason: on request (off-topic bulk delete)
YouTube: https://www.youtube.com/incog_aoe
Garja wrote:
20 Mar 2020, 21:46
I just hope DE is not going to implement all of the EP changes. Right now it is a big clusterfuck.
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Re: Mathematics

Post by Jam »

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Nauru Dolan
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Re: Mathematics

Post by Dolan »


That's statistics not math.

Statistics is the science according to which, on average, every person on the planet has one testicle.
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Re: Mathematics

Post by howlingwolfpaw »

Dolan wrote:

That's statistics not math.

Statistics is the science according to which, on average, every person on the planet has one testicle.


So no MATH is used to determine statistics? Pretty sure you need too ADD all the number of people surveyed . Then SUBTRACT the difference of people with 1, zero or more testis, and then DIVIDE the 2 numbers to derive a PERCENT average. That's using math....

The science part is examining each patient to determine their physiology of numerical testis
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Re: Mathematics

Post by BrookG »

ovi12 wrote:
BrookG wrote:
ovi12 wrote:Anyone have any cool problems they would like to share? I just did a pretty cool one, the proof is easy if you know how to start it but finding the right direction to start in may or may not take some time. I saw this problem before a few years ago and I had to look up the solution, but I tried solving it now again and found another way to do it:

If S is the sum of two positive integers, show that 2S and 5S are the sum of 2 positive integers as well.

I think it's obvious they are sum of 2 positive integers. :hmm: Maybe you mean something like odd or even?

Lol wtf was i writing i meant squares. If S can be expressed as the sum of two squares, show that 2S can be expressed as the sum of two squares, and show that 5S can be expressed as the sum of two squares (integers only ofc)

I thought about it and I have an issue. Say S=2, 2=1^2+1^2. 2S=4, it can't be expressed as an addition of perfect squares, haven't checked for subtraction.
Correlation doesn't mean causation.
http://www.tylervigen.com/spurious-correlations

"mr.brookg go buy jeans and goto the club with somppuli" - Princeofkabul, July 2018
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No Flag Jaeger
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Re: Mathematics

Post by Jaeger »

BrookG wrote:
ovi12 wrote:
Show hidden quotes

Lol wtf was i writing i meant squares. If S can be expressed as the sum of two squares, show that 2S can be expressed as the sum of two squares, and show that 5S can be expressed as the sum of two squares (integers only ofc)

I thought about it and I have an issue. Say S=2, 2=1^2+1^2. 2S=4, it can't be expressed as an addition of perfect squares, haven't checked for subtraction.

2^2+0^2. Addition is sufficient for any number
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Greece BrookG
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Re: Mathematics

Post by BrookG »

@ovi12 Ok I got it. Tbh I search a bit on wiki for an equation I didn't know (Diophantus' identity).
(1) Diophantus' identity (a^2+b^2)*(c^2+d^2)=(ac-bd)^2+(ad-bc)^2
Say S=a^2+b^2.
From (1) 2S=(1^2+1^2)(a^2+b^2)=(a-b)^2+(a+b)^2
5S=((1^2)+(2^2))(a^2+b^2)=(a-2b)^2+(2a-b)^2
Correlation doesn't mean causation.
http://www.tylervigen.com/spurious-correlations

"mr.brookg go buy jeans and goto the club with somppuli" - Princeofkabul, July 2018
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No Flag Jaeger
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Re: Mathematics

Post by Jaeger »

BrookG wrote:@ovi12 It's seem like cheating, using zero imo

Well in the statement of the problem I think I said I allowed any integers, and zero is an integer. I could see why you would call it "cheating" if zero was always one of the squares, but it's not. So I'll state the problem once more with all the restrictions and details in one post:

Show that if S can be written as the sum of two perfect squares (squares of any integers) then 2S can be written as the sum of two perfect squares, and 5S can be written as the sum of two perfect squares.
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Re: Mathematics

Post by BrookG »

Edited my post after a while ;-) Also works for pS=x^2+y^2, where p congruent to 1(mod4) from Fermat's theorem, which I saw recently on numberphile.
Correlation doesn't mean causation.
http://www.tylervigen.com/spurious-correlations

"mr.brookg go buy jeans and goto the club with somppuli" - Princeofkabul, July 2018
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Re: Mathematics

Post by Jaeger »

BrookG wrote:@ovi12 Ok I got it. Tbh I search a bit on wiki for an equation I didn't know (Diophantus' identity).
(1) Diophantus' identity (a^2+b^2)*(c^2+d^2)=(ac-bd)^2+(ad-bc)^2
Say S=a^2+b^2.
From (1) 2S=(1^2+1^2)(a^2+b^2)=(a-b)^2+(a+b)^2
5S=((1^2)+(2^2))(a^2+b^2)=(a-2b)^2+(2a-b)^2

Congrats, that's the solution I found a few years ago when I couldn't do it. Now I revisited the problem and I came up with this:
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Re: Mathematics

Post by Jaeger »

@BrookG Yeah Numberphile OP. Did you see the one line proof video? The actual proof, on numberphile2; it's pretty cool.

Also, how did you find that identity?
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Re: Mathematics

Post by BrookG »

ovi12 wrote:@BrookG Yeah Numberphile OP. Did you see the one line proof video? The actual proof, on numberphile2; it's pretty cool.

Also, how did you find that identity?

I was thinking about the prime as a sum of squares. Googled it. Then on wikia's page on the paragraph of Euler's proof it's the first criterion
Correlation doesn't mean causation.
http://www.tylervigen.com/spurious-correlations

"mr.brookg go buy jeans and goto the club with somppuli" - Princeofkabul, July 2018
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Re: Mathematics

Post by BrookG »

Number theory seems the hardest branch to grasp.
Correlation doesn't mean causation.
http://www.tylervigen.com/spurious-correlations

"mr.brookg go buy jeans and goto the club with somppuli" - Princeofkabul, July 2018
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No Flag Jaeger
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Re: Mathematics

Post by Jaeger »

BrookG wrote:Number theory seems the hardest branch to grasp.

Well it's not hard to understand the questions but it's very difficult to get the solutions. But I think counting problems are the easiest ones to make mistakes in, at least for beginners like me

Have you taken number theory yet?
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