Each of x, y, and z is a
positive integer.
Derive a parametric formula that provides all possible solutions to this equation:
- (x2+x+1)(y2+y+1) = (z2+z+1)
It looks like (t, (2t+1)^2, (4t^3 + 6t^2 + 5t + 1)) is a solution
(4t^3 + 6t^2 + 5t + 1)
Running x from 1 to 20 with y=(2x+1)^2 and large z shows:
x y z
1 9 16
2 25 67
3 49 178
4 81 373
5 121 676
6 169 1111
7 225 1702
8 289 2473
9 361 3448
10 441 4651
11 529 6106
12 625 7837
13 729 9868
14 841 12223
15 961 14926
16 1089 18001
17 1225 21472
18 1369 25363
19 1521 29698
20 1681 34501
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Posted by Larry
on 2022-05-27 09:08:38 |
a few more parametrized
