## Re: [PrimeNumbers] Re: Prime chains x-->Ax+B [puzzle 2]

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• Another 4 15/16 chains, bringing the current total to 16. Still no sign of a 16/16, which I was hoping that I would have found by now. ... [18*x + 466270385,
Message 1 of 143 , Jan 1, 2011
Another 4 15/16 chains, bringing the current total to 16.

Still no sign of a 16/16, which I was hoping that I would have found by now.

>[18*x + 4143491, [1989217, 15]]
>[18*x + 18192515, [1087, 15]]
>[18*x - 54818687, [16723501, 15]]
>[18*x + 76622095, [221831641, 15]]
>[18*x + 319862525, [25667359, 15]]
>[18*x + 386886155, [57802093, 15]]
>[18*x + 94904545, [132628157, 15]]
>[18*x + 102486395, [504312947, 15]]
>[18*x + 129499855, [444809429, 15]]
>[18*x + 270803885, [91364431, 15]]
>[18*x + 438255215, [413617013, 15]]
>[18*x + 500677507, [482332909, 15]]

[18*x + 466270385, [120478417, 15]]
[18*x + 615660455, [65330743, 15]]
[18*x + 645148609, [44282963, 15]]
[18*x + 904033405, [60651301, 15]]
• ... Suppose that we want to start with a square and get a square. Then we must solve the Diophantine equation y^2 = a*x^2 + b For any pair (a,b), Dario will
Message 143 of 143 , Jan 7, 2011
Kevin Acres <research@...> wrote:

> x=a*x+b either is a square or has a square as a major factor.

Suppose that we want to start with a square and get a square.
Then we must solve the Diophantine equation
y^2 = a*x^2 + b

For any pair (a,b), Dario will tell us all the solutions: