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 Showing results 1 to 25 of 1000 Search took 0.43 seconds. Search: Posts Made By: paulunderwood
 Forum: Miscellaneous Math 2020-09-19, 17:44 Replies: 93 Views: 7,907 Posted By paulunderwood A variation on the theme I have been considering x^2-2*x+2^r=0 and have been taking n+1 powers of x over it. I can also take n+1 powers over x^2-(4/2^r-2)+1 and expect the answer to be 1. This gives rise to (yet) another...
 Forum: Miscellaneous Math 2020-09-19, 09:04 Replies: 93 Views: 7,907 Posted By paulunderwood Letting r=1 is trivial as the Euler part becomes... Letting r=1 is trivial as the Euler part becomes Mod(-1)^((n-1)/2). Also it is specified gcd(2-2^r,n)==1 because of x^2-(2^2/2^r-2)*x+1 r=2 does not pass gcd(4-2^r,n)==1. This comes from...
 Forum: GpuOwl 2020-09-18, 09:56 Replies: 56 Views: 4,653 Posted By paulunderwood I think you should have decreased it. I think you should have decreased it.
 Forum: Miscellaneous Math 2020-09-17, 16:41 Replies: 93 Views: 7,907 Posted By paulunderwood Your idea seems right. I ran some of this: {... Your idea seems right. I ran some of this: { forstep(n=30169231,30169231,2, if(!ispseudoprime(n)&&!issquare(n), for(b=1,n,if(gcd(b,n)==1,z=znorder(Mod(b,n)); for(r=1,z,A=Mod(b,n)^r;...
 Forum: GpuOwl 2020-09-17, 05:24 Replies: 2,471 Views: 145,986 Posted By paulunderwood I can't help. I have never used colab. I can't help. I have never used colab.
 Forum: GpuOwl 2020-09-17, 05:18 Replies: 2,471 Views: 145,986 Posted By paulunderwood This is not a bash terminal. Are you using... This is not a bash terminal. Are you using "colab"?
 Forum: GpuOwl 2020-09-17, 05:05 Replies: 2,471 Views: 145,986 Posted By paulunderwood No no. At the terminal enter g++ --version ... No no. At the terminal enter g++ --version Also try g++ followed by hitting tab a couple of times.
 Forum: GpuOwl 2020-09-17, 04:43 Replies: 2,471 Views: 145,986 Posted By paulunderwood What does g++ --version say? You might have... What does g++ --version say? You might have to hardwire your compiler name and version in gpuOwl's makefile.
 Forum: Miscellaneous Math 2020-09-16, 13:42 Replies: 37 Views: 1,172 Posted By paulunderwood Once again it is meaningless to talk about... Once again it is meaningless to talk about "u>log(p)^2" when working with modular arithmetic. Also it makes absolutely no difference where you apply modulo operations. It is a "multiplicative...
 Forum: Miscellaneous Math 2020-09-15, 18:52 Replies: 93 Views: 7,907 Posted By paulunderwood Efficiencies Using Euler+Frobenius on x=1+-sqrt(1-b^4). For intermediate values s*x+t in left-right exponentiation of the Frobenius test we have:- Squaring: ? Mod(s*x+t,x^2-2*x+b^4)^2 Mod((2*s^2 + 2*t*s)*x +...
 Forum: Miscellaneous Math 2020-09-15, 15:50 Replies: 12 Views: 286 Posted By paulunderwood Mod(10,107)^10000000000000000000000000000000000000... Mod(10,107)^100000000000000000000000000000000000000000 Mod(34, 107) ## *** last result computed in 0 ms. It actually works by left-right binary exponentiation modulo n...
 Forum: Miscellaneous Math 2020-09-15, 15:21 Replies: 12 Views: 286 Posted By paulunderwood This Robert at his computer: :primenet: ... This Robert at his computer: :primenet: Know that a*b mod n is the same as (a mod n) * (b mod n) :smile:
 Forum: Miscellaneous Math 2020-09-15, 14:06 Replies: 93 Views: 7,907 Posted By paulunderwood I made a mistake: Case 4 of FLT... I made a mistake: Case 4 of FLT (https://en.wikipedia.org/wiki/Fermat%27s_Last_Theorem#Proofs_for_specific_exponents) uses the fact a^4-b^4 is never a square. So I have to flip the sign to get: ...
 Forum: Miscellaneous Math 2020-09-15, 10:44 Replies: 93 Views: 7,907 Posted By paulunderwood test based on FLT proof n=4 In the previous I had x=1+-sqrt(1-2^r). I note that 2^r-1 (r>1) is never a square. So what else is never a square? In his proof of FLT case n=4 Fermat showed a^4+b^4 is never a square, which leads me...
 Forum: Miscellaneous Math 2020-09-15, 09:06 Replies: 37 Views: 1,172 Posted By paulunderwood :smile: :smile:
 Forum: Lounge 2020-09-14, 01:27 Replies: 5 Views: 306 Posted By paulunderwood The B in IBM stands for Ben. The B in IBM stands for Ben.
 Forum: Miscellaneous Math 2020-09-13, 18:25 Replies: 9 Views: 360 Posted By paulunderwood (2^29-2)%232 174 :ermm: (2^29-2)%232 174 :ermm:
 Forum: Miscellaneous Math 2020-09-13, 17:29 Replies: 37 Views: 1,172 Posted By paulunderwood That might take some time However: ... That might take some time However: {forstep(n=1001*1001,100000000,2, if(!ispseudoprime(n), for(u=1000000,n, A=Mod(Mod([1+i,1;1,u],n),i^2+1); X=A^n;...
 Forum: Miscellaneous Math 2020-09-13, 17:05 Replies: 37 Views: 1,172 Posted By paulunderwood {forstep(n=9,77,2, if(!ispseudoprime(n), ... {forstep(n=9,77,2, if(!ispseudoprime(n), for(u=round(log(n)^2),n, A=Mod(Mod([1+i,1;1,u],n),i^2+1); X=A^n; R=lift(lift(trace(X*i)))%i; if(R==1||R==n-1, print([n,u,R])))))} [25, 11, 24] [25,...
 Forum: Miscellaneous Math 2020-09-12, 15:01 Replies: 37 Views: 1,172 Posted By paulunderwood n=3225601;A=Mod(Mod([1+x,1;1,0],n),x^2+1);B=Mod(Mo... n=3225601;A=Mod(Mod([1+x,1;1,0],n),x^2+1);B=Mod(Mod([1,1;1,x],n),x^2+1);R=lift(lift(A^n-B^n));print(R) [x, 0; 0, 3225600*x] Your "theorem" is wrong.
 Forum: Miscellaneous Math 2020-09-11, 16:56 Replies: 37 Views: 1,172 Posted By paulunderwood The characteristic equations of the matrices are:... The characteristic equations of the matrices are: x^2 - (1+u)*x + u-1 == 0 and x^2 - (1+w)*x + w-1 == 0 The "residuals" depend on the jacobi symbol of the discriminants of these equations: ...
 Forum: Miscellaneous Math 2020-09-11, 16:15 Replies: 37 Views: 1,172 Posted By paulunderwood [n,u,w]=[1247, 601,... [n,u,w]=[1247, 601, 638];Mod([1,1;1,u],n)^(n)==[u,-1;-1,1]&&Mod([1,1;1,w],n)^(n)==[1,1;1,w] 1 I will have to think more about what you are writing.
 Forum: Miscellaneous Math 2020-09-11, 14:47 Replies: 37 Views: 1,172 Posted By paulunderwood [n,u]=[231, 65];Mod([1,1;1,u],n)^n==[u,-1;-1,1] ... [n,u]=[231, 65];Mod([1,1;1,u],n)^n==[u,-1;-1,1] 1 Theorem 1 also works for composites. Testing (n-1)/2 times with different u is infeasible for large n. Theorem 2 is ill-defined. What are...
 Forum: GPU Computing 2020-09-11, 14:19 Replies: 350 Views: 23,567 Posted By paulunderwood A nice looking rig with a great PSU. Send us... A nice looking rig with a great PSU. Send us another picture when you've installed the other R VII's, I particularly like the way the disk is just hanging about!
 Forum: Miscellaneous Math 2020-09-10, 05:04 Replies: 93 Views: 7,907 Posted By paulunderwood C++ code I have attached the C/C++ code I am using to verify the above test. I would appreciate any ideas for improvements that can be done. One idea is to have a threshold based on the size of z. If the...
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