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seen Apr 15 at 22:58

May
22
accepted If $x^2\equiv 1 \pmod{n}$ and $x \not\equiv \pm 1 \pmod{n}$, then either $\gcd(x-1,n)$ or $\gcd(x+1,n)$ is a nontrivial factor of n
May
22
awarded  Scholar
May
22
accepted RSA cryptosystem: If $k$ is a multiple of $\phi(N)$, then $k=2^t r$ with $r$ odd and $t\geq1$
May
22
comment If $x^2\equiv 1 \pmod{n}$ and $x \not\equiv \pm 1 \pmod{n}$, then either $\gcd(x-1,n)$ or $\gcd(x+1,n)$ is a nontrivial factor of n
Thanks! I'm new to number theory, so I have some questions. Why the latter assumption implies that $\gcd$s are $<n$? And why every nontrivial, proper divisor of n is prime?
May
22
revised If $x^2\equiv 1 \pmod{n}$ and $x \not\equiv \pm 1 \pmod{n}$, then either $\gcd(x-1,n)$ or $\gcd(x+1,n)$ is a nontrivial factor of n
added 4 characters in body
May
22
comment If $x^2\equiv 1 \pmod{n}$ and $x \not\equiv \pm 1 \pmod{n}$, then either $\gcd(x-1,n)$ or $\gcd(x+1,n)$ is a nontrivial factor of n
@JyrkiLahtonen: Yes, you're right! I'm studying an RSA problem and trying to understand the proof of the Fact 1 on page 205 from this paper.
May
22
revised If $x^2\equiv 1 \pmod{n}$ and $x \not\equiv \pm 1 \pmod{n}$, then either $\gcd(x-1,n)$ or $\gcd(x+1,n)$ is a nontrivial factor of n
added 109 characters in body; edited title
May
22
comment If $x^2\equiv 1 \pmod{n}$ and $x \not\equiv \pm 1 \pmod{n}$, then either $\gcd(x-1,n)$ or $\gcd(x+1,n)$ is a nontrivial factor of n
Oops, sorry. I'm reading this article and may have misinterpreted the problem.
May
22
asked If $x^2\equiv 1 \pmod{n}$ and $x \not\equiv \pm 1 \pmod{n}$, then either $\gcd(x-1,n)$ or $\gcd(x+1,n)$ is a nontrivial factor of n
May
21
asked RSA cryptosystem: If $k$ is a multiple of $\phi(N)$, then $k=2^t r$ with $r$ odd and $t\geq1$
Apr
6
awarded  Popular Question
Mar
12
awarded  Informed
Jun
30
comment Is $3^n - 2^n$ composite for all integers $n \geq 6$?
@Mavris: Thank you! Do we know whether or not there are infinitely many primes of that form?
Jun
30
comment Is $3^n - 2^n$ composite for all integers $n \geq 6$?
Cameron Buie: Important remark! Byron Schmuland: Nice webpage! Thank you guys.
Jun
30
comment Is $3^n - 2^n$ composite for all integers $n \geq 6$?
Thanks! Can we prove that there are infinitely many prime of that form?
Jun
30
comment Is $3^n - 2^n$ composite for all integers $n \geq 6$?
Thanks! Are there infinitely many primes of the form $3^n - 2^n$?
Jun
30
comment Is $3^n - 2^n$ composite for all integers $n \geq 6$?
Thanks for your counterexample! :-)
Jun
30
asked Is $3^n - 2^n$ composite for all integers $n \geq 6$?
Jun
24
comment The set of all finite sequences of members of a countable set is also countable
Thanks! Your explanation was quite straightforward and detailed. Ι think that Ross Millikan's assignment is not well-defined due to the fact that $A$ might be equal to $\mathbb{Q}$. Then it could be $\prod_{k=0}^m p_k^{a_k} \notin \mathbb{N}$ for some $(a_0,a_1,...,a_m)$.
Jun
24
awarded  Supporter