All Questions
14 questions
1
vote
1
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362
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Primality test for numbers of the form $4k+3$
Can you prove or disprove the following claim:
Let $n$ be a natural number of the form $4k+3$ , and let $c$ be the smallest odd prime such that $\binom{c}{n}=-1$ , where $\binom{}{}$ denotes a Jacobi ...
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10
votes
0
answers
633
views
Primality testing using Chebyshev polynomials
Can you provide a proof or a counterexample for the claim given below?
Inspired by an alternative definition of the Frobenius primality test which is given in this paper I have formulated the ...
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2
votes
0
answers
96
views
if such counter example exists for Lehmer's totient problem could we prove that there are infinity of them or just finitely?
I asked this question one month Ago in MSE but no answer for existence of argument which show if such counter example exists we would have infinity of them or just finitely many examples
Lehmer's ...
4
votes
1
answer
182
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Primality test for specific class of $N=8k \cdot 3^n-1$
This question is related to my previous question.
Can you prove or disprove the following claim:
Let $P_m(x)=2^{-m}\cdot \left(\left(x-\sqrt{x^2-4}\right)^{m}+\left(x+\sqrt{x^2-4}\right)^{m}\right)$
...
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2
votes
1
answer
365
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Primality test for specific class of $N=8kp^n-1$
My following question is related to my question here
Can you provide a proof or a counterexample for the following claim :
Let $P_m(x)=2^{-m}\cdot \left(\left(x-\sqrt{x^2-4}\right)^{m}+\left(x+\...
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5
votes
1
answer
332
views
Conjectured primality test for specific class of $N=k \cdot 6^n+1$
Can you provide a proof or a counterexample for the claim given below?
Inspired by Theorem 5 in this paper I have formulated the following claim:
Let $N=k \cdot 6^n+1$ , $k<6^n$ and $\operatorname{...
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9
votes
1
answer
418
views
Conjectured primality test for specific class of $N=4kp^n+1$
Can you provide a proof or counterexample for the following claim?
Let $P_m(x)=2^{-m}\cdot((x-\sqrt{x^2-4})^m+(x+\sqrt{x^2-4})^m)$ .
Let $N= 4kp^{n}+1 $ where $k$ is a positive natural number , $...
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3
votes
0
answers
266
views
Conjectured primality test for numbers of the form $N=4 \cdot 3^n-1$
This is a repost of this question.
Can you provide proof or counterexample for the claim given below?
Inspired by Lucas-Lehmer primality test I have formulated the following claim:
Let $P_m(x)=2^{-m}\...
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2
votes
1
answer
839
views
Primality test for generalized Fermat numbers
This question is successor of Primality test for specific class of generalized Fermat numbers .
Can you provide a proof or a counterexample for the claim given below?
Inspired by Lucas–Lehmer–Riesel ...
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3
votes
1
answer
383
views
Primality test for specific class of $N=k \cdot b^n-1$
This question is successor of Compositeness test for specific class of $N=k \cdot b^n-1$ .
Can you provide a proof or a counterexample to the following claim :
Let $P_m(x)=2^{-m}\cdot \left(\left(...
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11
votes
2
answers
911
views
Primality test for specific class of Proth numbers
Can you provide a proof or a counterexample for the following claim :
Let $P_m(x)=2^{-m}\cdot \left(\left(x-\sqrt{x^2-4}\right)^{m}+\left(x+\sqrt{x^2-4}\right)^{m}\right)$
Let $N=k\cdot 2^n+1$ such ...
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2
votes
0
answers
306
views
Conjectured initial values of Inkeri's primality test for Fermat numbers
This is a repost of this question .
Can you provide a proof or a counterexample to the claim given below ?
First , we shall give a definition of the Inkeri's primality test for Fermat numbers :
...
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66
votes
3
answers
6k
views
Chebyshev polynomials of the first kind and primality testing
Can you provide a proof or a counterexample for the claim given below ?
Inspired by Agrawal's conjecture in this paper and by Theorem 4 in this paper I have formulated the following claim :
Let $...
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5
votes
0
answers
586
views
Primality test for specific class of generalized Fermat numbers
Can you provide a proof or a counterexample for the following claim :
Let $P_m(x)=2^{-m}\cdot((x-\sqrt{x^2-4})^m+(x+\sqrt{x^2-4})^m)$ .
Let $F_{p,n}= (2p)^{2^n}+1 $ where $p$ is a prime number ...
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