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Old 2022-10-23, 22:08   #45
R. Gerbicz
 
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Quote:
Originally Posted by paulunderwood View Post
Have you confirmed it with Pari/GP? Maybe his (JS?) code suffers from a flaw.
Nope, do not need to try it out, it would pass those checks also in Pari-Gp.
Btw, my first "counterexample" discovered when not even looked the source code of the page. There is not one type of check, so it takes time to figure out what it is actually doing.

Last fiddled with by R. Gerbicz on 2022-10-23 at 22:08
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Old 2022-10-23, 22:16   #46
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Nope, do not need to try it out, it would pass those checks also in...
Yeah. Realatively simple.

Somewhat similar.
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Old 2022-10-23, 22:34   #47
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Originally Posted by Batalov View Post
In most implementations, you don't know c or z. And why would scan over those? Wasteful.

It is simpler than that, you sum ax + by, then run any implementation of ispower() on the result and ispower() will return 1 or 2 (which is of no use) ... or >2 and only then you have the solution.

With the disclaimer that this is just an answer to "your" approach. The real approach is that there are tons of theoretical results on restrictions on what triples are even eligible to start search. Those should be used and that will be 99% of the code. Checking a double for loop with ispower() inside is <1% of the "code".
On the newer page it is not quite clear what Peter Norvig is actually doing, but in fact he is doing (almost) the same thing what he has done in the past: http://norvig.com/beal2000.html . So search A,B,C for some M limit and exponents X,Y,Z to another E limit, what is in the new code is that for some reason he considered only the exponent=4 or prime>2.

In this way he was able to do the check in only (average) O(1) time for each sum, exactly O(1) time is also possible. And note also that to compute the "sum" is also in O(1) time, since he considered the sum only mod m, for some fixed m. These are quite unreachable times with an ispower() routine, since C>M or exponent>E is possible.
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Old 2022-10-24, 13:56   #48
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Moderator note: Thread moved to OP's blog on the grounds there is no mathematical content,
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Old 2022-10-24, 20:57   #49
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Moderator note: Thread moved to OP's blog on the grounds there is no mathematical content,
Some jolly good fun in there, though... 9-)
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Old 2022-10-25, 15:46   #50
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Some jolly good fun in there, though... 9-)
Ditto! Not everything has to have mathematical content. This place would be really dry if it did.
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