To: Craig D,
Quoting Craig D:
Quote:
How'd you do that, Don?!
Not only is this a solution, the program in post #5 confirms that
it’s the first solution – that is, 353 is the least for which a solution exists.
How did you find it? It took my program nearly 23 million operations
(nearly 5 minutes on my clunky old 2004 laptop) to find this
(it’s a lot faster when told to ignore than the hour or so it took to find
a solution ignoring only greater than it has already found).
Unless you’re using a computer program, or you’re a neuroatypical savant,
you’ve got to be using some techniques (or intuitions) much better than my program’s,
as humans can’t check millions of numbers overnight!
Inquiring minds want to know how you did it.
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I don't own a computer and never even touched one until recently,
so I can't help with "programs", "computer searches" and the like.
However, I do know how to post in forums, check my e-mails, and "Google search".
Now, if you do a "Google search" on "Diophantine equations fourth powers",
then you will find the solution that I posted, and many other solutions as well!
(Wolfram has seperate articles on "second powers", "third powers", etc.)
For me, the most interesting solutions are those where
no two terms share a common factor, but so far,
the only such solutions that I found are confined to
"second power Diophantine equations".
By the way, I have never ever heard it conjectured that
"absolute co-primality" is a property that is exclusive to
"second power Diophantine equations",
so let's be on the lookout for a counter example.
Don.
