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 2020-09-09, 15:59 #1 Alberico Lepore     May 2017 ITALY 1DB16 Posts "New" same approach that isn't factorization a * b = N if N mod 4 = 1 then 2 * N + 2 * a ^ 2 + ((b-a) / 2) ^ 2 = ((3 * a + b) / 2) ^ 2 now i found that in some cases (i don't know which ones) this is also true 2 * N + 2 * 1 ^ 2 + y ^ 2 - ((3 * a + b) / 2) ^ 2 = 0 So for example for the case N = 65 you would 2 * 65 + 2 * a ^ 2 + ((b-a) / 2) ^ 2 = ((3 * a + b) / 2) ^ 2 , a * b = 65 , 130 + 2 * 1 ^ 2 + y ^ 2 - ((3 * a + b) / 2) ^ 2 = 0 Could you help me: 1) When is this true? 2 * N + 2 * 1 ^ 2 + y ^ 2 - ((3 * a + b) / 2) ^ 2 = 0 2) How would you fix the system?
2020-09-09, 19:59   #2
xilman
Bamboozled!

"πΊππ·π·π­"
May 2003
Down not across

10,639 Posts

Quote:
 Originally Posted by Alberico Lepore 2) How would you fix the system?
You should fix it by doing far more work before spewing out your posts.

2020-09-09, 20:13   #3
Alberico Lepore

May 2017
ITALY

52×19 Posts

Quote:
 Originally Posted by Alberico Lepore 1) When is this true? 2 * N + 2 * 1 ^ 2 + y ^ 2 - ((3 * a + b) / 2) ^ 2 = 0
Quote:
 Originally Posted by xilman You should fix it by doing far more work before spewing out your posts.
When is this true?

2020-09-09, 20:17   #4
VBCurtis

"Curtis"
Feb 2005
Riverside, CA

2·5·11·43 Posts

Quote:
 Originally Posted by Alberico Lepore When is this true?
Only on the 4th Friday of each month. By extension, that's the only day you should post.

2020-09-09, 20:32   #5
chalsall
If I May

"Chris Halsall"
Sep 2002

24×5×7×17 Posts

Quote:
 Originally Posted by VBCurtis Only on the 4th Friday of each month. By extension, that's the only day you should post.
I would recommend only on the 5th Friday of a month...

Just wondering why this troll is being allowed to continue to post noise? Even after he pledged to stop doing so...

2020-09-09, 21:13   #6
Uncwilly
6809 > 6502

"""""""""""""""""""
Aug 2003
101Γ103 Posts

100101000001102 Posts

Quote:
 Originally Posted by chalsall Just wondering why this troll is being allowed to continue to post noise? Even after he pledged to stop doing so...
Because only Thor can lift that ban hammer and has not chosen to do so.

2020-09-10, 00:47   #7
CRGreathouse

Aug 2006

32×5×7×19 Posts

Quote:
 Originally Posted by Alberico Lepore a * b = N if N mod 4 = 1
$$ab \equiv 1 \pmod4,$$ so either $$a \equiv b \equiv 1 \pmod4$$ or $$a \equiv b \equiv 3 \pmod4$$.

Quote:
 Originally Posted by Alberico Lepore then 2 * N + 2 * a ^ 2 + ((b-a) / 2) ^ 2 = ((3 * a + b) / 2) ^ 2
$2ab + 2a^2 + (b^2 - 2ab + a^2)/4 = (9a^2 + 6ab + b^2)/4$

Yep, this checks out, both as an identity and with the relevant quantities as multiples of 4.

Quote:
 Originally Posted by Alberico Lepore now i found that in some cases (i don't know which ones) this is also true 2 * N + 2 * 1 ^ 2 + y ^ 2 - ((3 * a + b) / 2) ^ 2 = 0
Are you asking for which y this equality holds?

2020-09-10, 07:19   #8
Alberico Lepore

May 2017
ITALY

52×19 Posts

Quote:
 Originally Posted by CRGreathouse Are you asking for which y this equality holds?
What characteristic must N have for that equality to be true

for example for N = 121

this

2 * 121 + 2 * 1 ^ 2 + y ^ 2- (22) ^ 2 = 0

it's not true

that is, y is not integer

Last fiddled with by Alberico Lepore on 2020-09-10 at 07:22

2020-09-10, 07:25   #9
retina
Undefined

"The unspeakable one"
Jun 2006
My evil lair

6,113 Posts

Quote:
 Originally Posted by Alberico Lepore ... N = 65
What? Back to this uselessness again!

I thought you had promoted yourself to 18 digit numbers. What happened to that?

2020-09-10, 08:32   #10
Alberico Lepore

May 2017
ITALY

52·19 Posts

Quote:
 Originally Posted by retina What? Back to this uselessness again! I thought you had promoted yourself to 18 digit numbers. What happened to that?
I have not abandoned CRGreathouse number

390644893234047643=4*K+3

390644893234047643*3=1171934679702142929=4*H+1

Now I need to understand what k values this system returns integer values

a*b=1171934679702142929*(4*k+1)
,
2*1171934679702142929*(4*k+1)+2*a^2+((b-a)/2)^2-z^2=0
,
2*1171934679702142929*(4*k+1)+2*1^2+y^2-z^2=0

Last fiddled with by Alberico Lepore on 2020-09-10 at 08:34

2020-09-10, 08:37   #11
retina
Undefined

"The unspeakable one"
Jun 2006
My evil lair

611310 Posts

Quote:
 Originally Posted by Alberico Lepore I have not abandoned CRGreathouse number
Good. So why all this useless N=65 stuff?
Quote:
 Originally Posted by Alberico Lepore Now I need to understand what k values this system returns integer values
Well go on then, have at it.

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