Produce all solutions for $2a^2 + b^2 = c^2$

Asked Dec 24 '14 at 19:59

Active Dec 28 '14 at 03:13

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I'm trying to generate a stream of tuples $(a, b, c)$ that satisfy the equation $2a^2 + b^2 = c^2$

The first $10$ results are:

$2, 1, 3$

$4, 2, 6$

$6, 3, 9$

$4, 7, 9$

$6, 7, 11$

$8, 4, 12$

$10, 5, 15$

$12, 1, 17$

$12, 6, 18$

$8, 14, 18$

There is a solution for $x_2+2y_2=z_2$ which is exactly the same but I cannot understand how I can produce all these numbers as a function. For instance, it says $x_3=(a_2+2b_2)t=3$ which is the solution of $c$, in my case, but it includes $x_3$ because $t = \dfrac{1}{2}(x_1+x_3)$. In addition, he gives the values $\{x_1,x_2,x_3\} = \{1,2,3\}$ but I'm not sure which are the next values. Any help please. Thank you in advance!!!

edited Dec 28 '14 at 03:13

Praveen

1,613

asked Dec 24 '14 at 19:59

jimakos17

What do you mean by the "first" ten? How are you indexing them? – John Dec 24 '14 at 20:07
2

see http://math.stackexchange.com/questions/367443/find-all-solutions-x2-2y2-z2 – Will Jagy Dec 24 '14 at 20:17
It is ordered by increasing values of c. If two tuples result in the same value of c, then is sorted by increasing orders of b. – jimakos17 Dec 24 '14 at 20:30

Produce all solutions for $2a^2 + b^2 = c^2$

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