Forum: Miscellaneous Math
2022-08-19, 19:23
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Replies: 8
Views: 325
Summarizing the two cases:
n%8=3 ::...
Summarizing the two cases:
n%8=3 :: 2^((n-1)/2) == -1 mod n :: z is even :: two solutions exist: z and z/2
n%8=7 :: 2^((n-1)/2 == 1 mod n :: z is odd :: one solution exists.
Due to z being on...
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Forum: Miscellaneous Math
2022-08-19, 14:18
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Replies: 8
Views: 325
On this theme, since n==3 mod 4 then n-1 is...
On this theme, since n==3 mod 4 then n-1 is divisible by 2 and not 4. Then the only possible strengthening is a base 2 Euler PRP. That is up to multiplicative order, there seems to be one or two...
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Forum: Miscellaneous Math
2022-08-19, 04:47
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Replies: 8
Views: 325
A small observation: If a number n==3 mod 4 is...
A small observation: If a number n==3 mod 4 is Fermat 2-PRP then 2^(n-1)==1 mod n. If z is the multiplicative order of 2 mod n, then z divides n-1. Also (x+2^z) == x+1 mod n. Furthermore, (x+1)^(n+1)...
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Forum: Miscellaneous Math
2022-08-18, 15:26
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Replies: 8
Views: 325
Recap: I am testing: Fermat 2-prp and...
Recap: I am testing: Fermat 2-prp and (x+2^r)^(n+1)==4^r+1 where gcd(r,n-1)==1, and have reached n<4*10^14 without counterexample.
Now, writing a=lift(Mod(2,n)^r) the Lucas part can be written as...
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Forum: And now for something completely different
2022-08-07, 17:52
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Replies: 188
Views: 14,426
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Forum: Linux
2022-08-03, 22:31
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Replies: 10
Views: 691
I have never used screen before and am just...
I have never used screen before and am just playing around with it now. It seems you want sudo crontab -e (or root's account) and enter there @reboot su math-user -c "cd /your/path && screen...
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Forum: And now for something completely different
2022-08-02, 23:31
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Replies: 49
Views: 10,684
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Forum: Linux
2022-08-02, 11:26
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Replies: 10
Views: 691
I see this as two problems: Firstly getting...
I see this as two problems: Firstly getting something to run at boot and secondly getting something to run when logging in.
For the first use @reboot su math-user -c "X" (in sudo crontab -e) where...
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Forum: Linux
2022-07-31, 18:51
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Replies: 10
Views: 691
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Forum: Chess
2022-07-24, 20:30
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Replies: 5
Views: 357
First Law of Robotics broken
The first law of robotics (https://en.wikipedia.org/wiki/Three_Laws_of_Robotics) has been broken. A 7 year boy has been injured playing chess...
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Forum: sweety439
2022-07-22, 21:39
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Replies: 13
Views: 562
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Forum: Riesel Prime Search
2022-07-22, 04:12
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Replies: 1,984
Views: 249,575
9473*2^4543680-1...
9473*2^4543680-1 (https://primes.utm.edu/primes/page.php?id=134201) (1367788 digits) found Vincent Diepeveen
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Forum: Proth Prime Search
2022-07-21, 14:42
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Replies: 1
Views: 248
6 million digits prime!
Congrats to Ryan for 7*2^20267500 + 1 (https://primes.utm.edu/primes/page.php?id=134192) with 6,101,127 digits and entrance rank 17 in top5000.
:banana: :banana: :banana: :banana: :banana:...
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Forum: science_man_88
2022-07-20, 20:46
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Replies: 2
Views: 232
WB sm88.
I never know if to use my or local,...
WB sm88.
I never know if to use my or local, but your code can be made better by:
div(n,x)=local(tz=10^znorder(Mod(10,x)));if(n<=tz,return(n),return(n%tz+div(floor(n/tz),x)))
I think znorder...
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Forum: Miscellaneous Math
2022-07-19, 18:03
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Replies: 8
Views: 325
Let z=znorder(Mod(2,n)).
Then...
Let z=znorder(Mod(2,n)).
Then [2^(z-r),-1;1,2^(z-r)]^(n+1) == 4^(z-r)+1 == (4^z+4^r)/(4^r) == (1+4^r)/4^r all mod n
So 2^(r*(n+1))*[2^-r,-1;1,2^-r]^(n+1) = (1+4^r)*2^(r*(n-1)) mod n
Or...
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Forum: Miscellaneous Math
2022-07-18, 23:48
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Replies: 8
Views: 325
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Forum: Miscellaneous Math
2022-07-18, 18:26
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Replies: 8
Views: 325
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Forum: Miscellaneous Math
2022-07-17, 20:34
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Replies: 8
Views: 325
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Forum: Miscellaneous Math
2022-07-17, 16:29
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Replies: 8
Views: 325
3 mod 4 with free parameter
Consider [a,-1;1,a] = 2*a + [-a,-1;1,-a] where M=[a,-1;1,a] has the character x^2-2*a*x+a^2+1 and its discriminant = -1. Solving the character gives x=a+-sqrt(-1), leading to a test:
...
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Forum: And now for something completely different
2022-07-17, 08:07
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Replies: 49
Views: 10,684
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Forum: Information & Answers
2022-07-16, 16:51
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Replies: 16
Views: 511
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Forum: Information & Answers
2022-07-16, 15:24
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Replies: 16
Views: 511
It is not unknown that sometimes a CPU needs...
It is not unknown that sometimes a CPU needs reseating. This will also ensure you have perfect contact between the CPU and the heatsink, separted by the thinnest layer of paste when you reinstall the...
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Forum: And now for something completely different
2022-07-16, 07:01
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Replies: 49
Views: 10,684
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Forum: sweety439
2022-07-15, 10:27
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Replies: 13
Views: 562
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Forum: And now for something completely different
2022-07-14, 06:57
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Replies: 49
Views: 10,684
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