20221010, 00:37  #1 
Sep 2002
Database er0rr
2×3^{3}×83 Posts 
Double Cubic Frobenius Trinomial test
Let the test be:
Code:
{tst(n,a,b)=c=a+b;T=(xa)*(xb)*(x+c); trace(Mod(Mod(x,n),T1)^n)==0&& trace(Mod(Mod(x,n),T+1)^n)==0} I have also run: Code:
for(n=4,10000000,if(!ispseudoprime(n)&&tst(n,1,2),print([n,factor(n)]))) [49, Mat([7, 2])] [343, Mat([7, 3])] [2401, Mat([7, 4])] [16807, Mat([7, 5])] [84035, [5, 1; 7, 5]] [98441, [7, 4; 41, 1]] [117649, Mat([7, 6])] [232897, [7, 4; 97, 1]] [823543, Mat([7, 7])] [5764801, Mat([7, 8])] It's a fun test to play with! 
20221010, 08:31  #2  
Sep 2002
Database er0rr
1000110000010_{2} Posts 
Quote:


20221010, 13:41  #3  
Sep 2002
Database er0rr
2×3^{3}×83 Posts 
Quote:
For example a=3*17 and b=3*17 produces numbers only divisible by D=17. But what is D for various A and B? Especially for A!=B? Last fiddled with by paulunderwood on 20221010 at 13:45 

20221010, 15:48  #4  
Sep 2002
Database er0rr
2·3^{3}·83 Posts 
Quote:
Code:
for(v=1,#V,n=V[v];if(tst(n,16,16),print([n,factor(n)]))) Last fiddled with by paulunderwood on 20221010 at 16:02 

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