Find a non-trivial integer solution to this equation:
x2 - 181y2 = 1.
From my solution to http://perplexus.info/show.php?pid=4338&cid=70423:
The continued fraction expansion of sqrt(181) = [13; 2, 4, 1, 8, 6, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 6, 8, 1, 4, 2, 26]
This period is odd, so we need to determine the rational convergent to sqrt(181) up to the end of the second period:
[13; 2, 4, 1, 8, 6, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 6, 8, 1, 4, 2, 26, 2, 4, 1, 8, 6, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 6, 8, 1, 4, 2] = 2469645423824185801/183567298683461940
So the x and y values are respectively 2469645423824185801 and 183567298683461940.
Checking: 2469645423824185801^2-1=181*183567298683461940^2 / true
Edited on June 13, 2024, 10:34 am
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Posted by broll
on 2024-06-13 10:33:26 |
Possible Solution