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 Alberico Lepore 2022-01-16 19:36

Strange coincidence on prime numbers

Strange coincidence on prime numbers

 Alberico Lepore 2022-01-16 23:44

Signore e signori et voila

 Alberico Lepore 2022-01-17 20:41

[QUOTE=Alberico Lepore;598127]Signore e signori et voila

131 primo una soluzione che si ripete ogni due volta
solve integer [(8*k+1)*((8*k+1)+2)-4*(3*x^2+4*x+1)]-131 =0 ,x>0 , k>0
[url]https://www.wolframalpha.com/input/?i=solve+integer+%5B%288*k%2B1%29*%28%288*k%2B1%29%2B2%29-4*%283*x%5E2%2B4*x%2B1%29%5D-131+%3D0+%2Cx%3E0+%2C+k%3E0+[/url]

17891 primo due soluzioni che si ripetono ogni quattro volte
solve integer [(8*k+1)*((8*k+1)+2)-4*(3*x^2+4*x+1)]-17891 =0 ,x>0 , k>0
[url]https://www.wolframalpha.com/input/?i=solve+integer+%5B%288*k%2B1%29*%28%288*k%2B1%29%2B2%29-4*%283*x%5E2%2B4*x%2B1%29%5D-17891+%3D0+%2Cx%3E0+%2C+k%3E0+[/url]

26179 non primo una soluzione che si ripete ogni tre volte
solve integer [(8*k+1)*((8*k+1)+2)-4*(3*x^2+4*x+1)]-26179 =0 ,x>0 , k>0
[url]https://www.wolframalpha.com/input/?i=solve+integer+%5B%288*k%2B1%29*%28%288*k%2B1%29%2B2%29-4*%283*x%5E2%2B4*x%2B1%29%5D-26179+%3D0+%2Cx%3E0+%2C+k%3E0+[/url]

12931 non primo non so cosa succede
solve integer [(8*k+1)*((8*k+1)+2)-4*(3*x^2+4*x+1)]-12931 =0 ,x>0 , k>0
[url]https://www.wolframalpha.com/input/?i=solve+integer+%5B%288*k%2B1%29*%28%288*k%2B1%29%2B2%29-4*%283*x%5E2%2B4*x%2B1%29%5D-12931+%3D0+%2Cx%3E0+%2C+k%3E0+[/url]

 Alberico Lepore 2022-01-17 21:10

[QUOTE=Alberico Lepore;598227]131 primo una soluzione che si ripete ogni due volta
solve integer [(8*k+1)*((8*k+1)+2)-4*(3*x^2+4*x+1)]-131 =0 ,x>0 , k>0
[url]https://www.wolframalpha.com/input/?i=solve+integer+%5B%288*k%2B1%29*%28%288*k%2B1%29%2B2%29-4*%283*x%5E2%2B4*x%2B1%29%5D-131+%3D0+%2Cx%3E0+%2C+k%3E0+[/url]

17891 primo due soluzioni che si ripetono ogni quattro volte
solve integer [(8*k+1)*((8*k+1)+2)-4*(3*x^2+4*x+1)]-17891 =0 ,x>0 , k>0
[url]https://www.wolframalpha.com/input/?i=solve+integer+%5B%288*k%2B1%29*%28%288*k%2B1%29%2B2%29-4*%283*x%5E2%2B4*x%2B1%29%5D-17891+%3D0+%2Cx%3E0+%2C+k%3E0+[/url]

26179 non primo una soluzione che si ripete ogni tre volte
solve integer [(8*k+1)*((8*k+1)+2)-4*(3*x^2+4*x+1)]-26179 =0 ,x>0 , k>0
[url]https://www.wolframalpha.com/input/?i=solve+integer+%5B%288*k%2B1%29*%28%288*k%2B1%29%2B2%29-4*%283*x%5E2%2B4*x%2B1%29%5D-26179+%3D0+%2Cx%3E0+%2C+k%3E0+[/url]

12931 non primo non so cosa succede
solve integer [(8*k+1)*((8*k+1)+2)-4*(3*x^2+4*x+1)]-12931 =0 ,x>0 , k>0
[url]https://www.wolframalpha.com/input/?i=solve+integer+%5B%288*k%2B1%29*%28%288*k%2B1%29%2B2%29-4*%283*x%5E2%2B4*x%2B1%29%5D-12931+%3D0+%2Cx%3E0+%2C+k%3E0+[/url][/QUOTE]

Soluzioni ricorsive

k(n+1) = 97 ⁢k(n) + 42 x(n) + 52 ⁢

x(n+1) = 224 k(n) + 97 ⁢x(n) + 120 ⁢

k(n+1) = 97 ⁢k(n) - 42 ⁢x(n) - 4 ⁢

x(n+1) = - 224 ⁢k(n) + 97 ⁢x(n) + 8

 Alberico Lepore 2022-01-18 16:09

[QUOTE=Alberico Lepore;598127]Signore e signori et voila