Beal's conjecture prize - Page 5

R. Gerbicz · 2022-10-23, 22:08

Quote:

Originally Posted by paulunderwood

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.

chalsall · 2022-10-23, 22:16

Quote:

Originally Posted by R. Gerbicz

Nope, do not need to try it out, it would pass those checks also in...

Yeah. Realatively simple.

Somewhat similar.

R. Gerbicz · 2022-10-23, 22:34

Quote:

Originally Posted by Batalov

In most implementations, you don't know c or z. And why would scan over those? Wasteful.

It is simpler than that, you sum a^x + b^y, 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.

paulunderwood · 2022-10-24, 13:56

Moderator note: Thread moved to OP's blog on the grounds there is no mathematical content,

chalsall · 2022-10-24, 20:57

Quote:

Originally Posted by paulunderwood

Moderator note: Thread moved to OP's blog on the grounds there is no mathematical content,

Some jolly good fun in there, though... 9-)

storm5510 · 2022-10-25, 15:46

Quote:

Originally Posted by chalsall

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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2022-10-24, 13:56	#48
paulunderwood Sep 2002 Database er0rr 2⁴×281 Posts	Moderator note: Thread moved to OP's blog on the grounds there is no mathematical content,