mersenneforum.org (https://www.mersenneforum.org/index.php)
-   Alberico Lepore (https://www.mersenneforum.org/forumdisplay.php?f=166)
-   -   "New" same approach that isn't factorization (https://www.mersenneforum.org/showthread.php?t=25940)

 Alberico Lepore 2020-09-09 15:59

"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?

 xilman 2020-09-09 19:59

[QUOTE=Alberico Lepore;556558]2) How would you fix the system?[/QUOTE]You should fix it by doing far more work before spewing out your posts.

 Alberico Lepore 2020-09-09 20:13

[QUOTE=Alberico Lepore;556558]
1) When is this true?

2 * N + 2 * 1 ^ 2 + y ^ 2 - ((3 * a + b) / 2) ^ 2 = 0

[/QUOTE]

[QUOTE=xilman;556588]You should fix it by doing far more work before spewing out your posts.[/QUOTE]

When is this true?

 VBCurtis 2020-09-09 20:17

[QUOTE=Alberico Lepore;556589]When is this true?[/QUOTE]

Only on the 4th Friday of each month. By extension, that's the only day you should post.

 chalsall 2020-09-09 20:32

[QUOTE=VBCurtis;556590]Only on the 4th Friday of each month. By extension, that's the only day you should post.[/QUOTE]

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...

 Uncwilly 2020-09-09 21:13

[QUOTE=chalsall;556592]Just wondering why this troll is being allowed to continue to post noise? Even after he pledged to stop doing so...[/QUOTE]Because only Thor can lift that ban hammer and has not chosen to do so.

 CRGreathouse 2020-09-10 00:47

[QUOTE=Alberico Lepore;556558]a * b = N

if N mod 4 = 1[/QUOTE]

[$]ab \equiv 1 \pmod4,[/$] so either [$]a \equiv b \equiv 1 \pmod4[/$] or [$]a \equiv b \equiv 3 \pmod4[/$].

[QUOTE=Alberico Lepore;556558]then 2 * N + 2 * a ^ 2 + ((b-a) / 2) ^ 2 = ((3 * a + b) / 2) ^ 2[/QUOTE]

[$$]2ab + 2a^2 + (b^2 - 2ab + a^2)/4 = (9a^2 + 6ab + b^2)/4[/$$]

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

[QUOTE=Alberico Lepore;556558]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[/QUOTE]

Are you asking for which y this equality holds?

 Alberico Lepore 2020-09-10 07:19

[QUOTE=CRGreathouse;556596]

Are you asking for which y this equality holds?[/QUOTE]

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

 retina 2020-09-10 07:25

[QUOTE=Alberico Lepore;556558]... N = 65[/QUOTE]What? Back to this uselessness again!

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

 Alberico Lepore 2020-09-10 08:32

[QUOTE=retina;556615]What? Back to this uselessness again!

I thought you had promoted yourself to 18 digit numbers. What happened to that?[/QUOTE]

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

 retina 2020-09-10 08:37

[QUOTE=Alberico Lepore;556617]I have not abandoned CRGreathouse number[/QUOTE]Good. So why all this useless N=65 stuff?[QUOTE=Alberico Lepore;556617]Now I need to understand what k values this system returns integer values[/QUOTE]Well go on then, have at it.

All times are UTC. The time now is 10:44.