Forum: Number Theory Discussion Group
2021-07-06, 11:45
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Replies: 9
Views: 1,774
Great explanation from the given subforum. ...
Great explanation from the given subforum.
About efficiently computing square roots modulo a large prime (hundreds of digits or more), there are two good algorithms by Tonelli-Shanks and by Cipolla.
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Forum: Puzzles
2021-07-01, 03:25
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Replies: 35
Views: 6,099
Actually, it seems that I spoiled it before....
Actually, it seems that I spoiled it before. Within this thread, I was the first one to say "Leyland" (should I say "xilman"?)
Wikipedia page about Leyland numbers mentions the largest known...
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Forum: Puzzles
2021-06-26, 04:41
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Replies: 35
Views: 6,099
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Forum: Puzzles
2021-06-22, 20:10
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Replies: 35
Views: 6,099
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Forum: Number Theory Discussion Group
2021-06-13, 08:51
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Replies: 10
Views: 3,020
With your "trigonometric" approach, you use...
With your "trigonometric" approach, you use integer parameters a and b to build a Pythagorean triplet A,B,C:
A = 2*a*b,
B = b^2 - a^2,
C = a^2 + b^2.
Then you generate a candidate solution:
x =...
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Forum: Puzzles
2021-03-20, 20:20
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Replies: 27
Views: 5,462
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Forum: Puzzles
2021-02-13, 04:25
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Replies: 27
Views: 5,462
Block-version is the most interesting one.
I...
Block-version is the most interesting one.
I slightly modifìed my candidate to fit your additional constraint.
Less words, but more symmetries.
86 words:
000100010001000
000100010001000...
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Forum: Puzzles
2021-02-08, 04:24
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Replies: 27
Views: 5,462
nice puzzle; not sure about minimality of my...
nice puzzle; not sure about minimality of my candidates.
"bars" version, fixing 150-word near-solution by Dr Sardonicus.
5 words and 4 bars per row/column;
150 words, 120 bars placed along 8...
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Forum: Puzzles
2020-12-06, 19:08
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Replies: 3
Views: 2,933
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Forum: Puzzles
2020-11-08, 07:57
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Replies: 34
Views: 9,351
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Forum: Puzzles
2020-11-08, 02:48
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Replies: 34
Views: 9,351
As an example, we can try to minimize code...
As an example, we can try to minimize code length.
In this sense, published solutions are hard to beat.
For base problem, we can save one line by applying the CHAOS trick described in post #23....
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Forum: Puzzles
2020-11-06, 03:12
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Replies: 34
Views: 9,351
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Forum: Puzzles
2020-11-05, 08:32
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Replies: 34
Views: 9,351
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Forum: Puzzles
2020-11-04, 17:30
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Replies: 34
Views: 9,351
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Forum: Puzzles
2020-10-23, 09:41
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Replies: 34
Views: 9,351
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Forum: Puzzles
2020-10-21, 11:10
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Replies: 34
Views: 9,351
I agree at 100% with you.
Had it been...
I agree at 100% with you.
Had it been necessary, writing it would have been too spoiling.
I only wrote that I found it useful (shorter code, faster reaching 1970)
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Forum: Puzzles
2020-10-21, 02:39
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Replies: 34
Views: 9,351
I wish I could call you "pessimistic".
Looking...
I wish I could call you "pessimistic".
Looking at the past three years, Oct20 seems somehow similar to Nov17, another "find-constrained-algorithm" challenge. Nov17 was actually solved by 23 people...
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Forum: Puzzles
2020-10-14, 09:04
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Replies: 34
Views: 9,351
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Forum: Puzzles
2020-10-12, 18:09
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Replies: 34
Views: 9,351
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Forum: Puzzles
2020-10-12, 03:06
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Replies: 33
Views: 14,073
I followed uau's suggestion.
Given a RPS(n)...
I followed uau's suggestion.
Given a RPS(n) game, we can always extend it to a RPS(n+2) game:
aaavw
aaavw
aaa10
ww001
vv100
where A is the adjacency matrix of the RPS(n) game, V is a column...
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Forum: Puzzles
2020-10-11, 10:31
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Replies: 33
Views: 14,073
After a slight modification, uau's "algebric"...
After a slight modification, uau's "algebric" construction also explains the RPS(13) game with 39 automorphisms (which is optimal, according to the paper referenced within September's solution)....
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Forum: Puzzles
2020-10-07, 05:28
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Replies: 33
Views: 14,073
A very elegant construction, thanks uau!
...
A very elegant construction, thanks uau!
Another nice construction works for composite n and solves n=9.
Given two games RPS(a) and RPS(b), build a game RPS(a*b).
Let z = x*b+y, with...
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Forum: Puzzles
2020-10-06, 10:53
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Replies: 33
Views: 14,073
As a lucky guess, I searched for RPS(n) games...
As a lucky guess, I searched for RPS(n) games which admit at least one n-cycle as an automorphism.
So they admit at least n automorphisms (by repeatedly applying the cyclic shift).
Can we get n*q...
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Forum: Puzzles
2020-10-06, 10:41
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Replies: 34
Views: 9,351
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Forum: Puzzles
2020-09-12, 03:25
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Replies: 33
Views: 14,073
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