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Search: Posts Made By: paulunderwood
Forum: Miscellaneous Math 2022-06-11, 11:54
Replies: 8
Views: 774
Posted By paulunderwood
I am running the following against Feitsma's...

I am running the following against Feitsma's Carmichael numbers list (2^64) with good results:

{for(a=3,1000,print([a]);f=x*(x-1)^3*(x^2-1)-a*(a-1)^3*(a^2-1);...
Forum: Miscellaneous Math 2022-06-10, 21:55
Replies: 8
Views: 774
Posted By paulunderwood
Let n = 2*(2^3-1)+c i.e. 14+c and test x^n = x...

Let n = 2*(2^3-1)+c i.e. 14+c and test x^n = x (mod n, x*(x^3-1)+c). Note this is not a necessary condition but I claim it is sufficient. Testing... [n,c]=[280067761, 280067747] is a counterexample....
Forum: Miscellaneous Math 2022-06-10, 17:15
Replies: 8
Views: 774
Posted By paulunderwood
Thanks for that link/info Dr. Sardoncus. I am...

Thanks for that link/info Dr. Sardoncus. I am unsure whether it is applicable or not.

I am now testing a quintic case on two fronts with gcd(c,n)==1 and positive n:


x^n == x (mod n, x^5-x-c)...
Forum: Miscellaneous Math 2022-06-10, 10:09
Replies: 8
Views: 774
Posted By paulunderwood
n=49141 and c=14695 is a counterexample. ...

n=49141 and c=14695 is a counterexample.

Clinging on... now testing x^n == x (mod n, x^4-x-c) where positive n = a^4-a-c for a in N and gcd(c,n)==1. However now n is much larger.

Edit: n =...
Forum: Miscellaneous Math 2022-06-10, 01:30
Replies: 8
Views: 774
Posted By paulunderwood
Now consider f=x^4-x-c where gcd(c,n)==1. So...

Now consider f=x^4-x-c where gcd(c,n)==1.

So to test odd "n" for primality find a "c" with gcd(c,n)==1 and compute x^n == x (mod n, x^4-x-c).

I am searching for a counterexample. :unsure:
...
Forum: Miscellaneous Math 2022-06-09, 23:43
Replies: 8
Views: 774
Posted By paulunderwood
Thinking about this x^3==x+1 and x+1 | x^3-x. ...

Thinking about this x^3==x+1 and x+1 | x^3-x.

Now consider only trinomials: let f=x^a-x^b-1 (a>b, a>3) and gcd(a,b)==1. For example f=x^5-x^3-1. Then x^5 == x^3+1 and gcd(x^3+1,x^5-x^3) = 1.

I...
Forum: Miscellaneous Math 2022-06-09, 21:13
Replies: 8
Views: 774
Posted By paulunderwood
Composite n=27664033 is x^n==x (mod n, x^3-x-1)....

Composite n=27664033 is x^n==x (mod n, x^3-x-1). :whistle:
Forum: Miscellaneous Math 2022-06-09, 11:56
Replies: 8
Views: 774
Posted By paulunderwood
A test for primality?

Over the years I have never found a counterexample to:

For integers x>1, s>=0, all r>0, all t>0, odd and irreducible \[f=(x^s\times\prod_{r,t}{(x^r-1)^t)}-1\] is x-PRP, except for the cases...
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