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My question relates, at least superficially, to these old ones: The value $\pm 1$ for the square root of Wilson's theorem, ((p-1)/2)! mod p Primes P such that ((P-1)/2)!=1 mod P When $p\equiv 1 \mo …

Suppose a non-real algebraic integer $\alpha$ has, aside from itself and its complex conjugate $\bar\alpha$, all its algebraic conjugates of norm less than 1. Then the fractional parts of $\Re(\alpha …

Roughly: Suppose you have a fraction $a/b$ and you expand it as a simple continued fraction $1/c_1+1/c_2\cdots+1/c_{n-1}+1/c_n$. Now truncate the last convergent and collapse $1/c_1+1/c_2\cdots+1/c_ …

Has $F(n)=\prod_{p\ {\rm prime}, p-1|n}p$ been studied? This function interests me because for each prime $p$, the long-term average number of factors of $p$ in $n$ equals the long-term average numbe …

Fix numbers $m, n, k\in {\Bbb Z}_+$ and $r\in {\Bbb R}_+$. What non-trivial estimates exist for the probability that a random $m\times n$ matrix, with integer entries and with all its rows of Eucli …

Does there exist an algorithm (of any complexity) for the following problem? Given: $p(x)\in{\Bbb Z}[x]$. Question: Does there exist a polynomial $q(x)= 1 - \sum_i^m x^{n_i}$ such that $p|q$? The va …

The $abc$-conjecture implies that the equation $a+b=c$ has only finitely many primitive solutions in the multiplicative semigroup generated by any particular finite set of primes. I would appreciate …

Faltings' theorem says (at least) that the set $C(K)$ of points of a higher genus curve $C$ rational over a number field $K$ constitutes a finite subset of the finitely generated (by Mordell-Weil) abe …

It seems natural to me to generalize the notion of perfect number to rings of integers more general that ${\Bbb Z}$. I'll want to think of number fields concretely, as subfields of ${\Bbb C}$. For a …

One can motivate Roth's theorem as follows. On $[0,1]$ consider the function $f$ that takes $x$ to the cardinality of the set { $p/q : |x - p/q | < 1/q^{2 + \epsilon}$ } . Now one can see that $\int …

For most of my life, one single (family of) Diophantine equation(s) dominated the list of the world's most celebrated unsolved mathematical problems. Perhaps the world we live in now has grown too so …

Title asks it: Does the Fourier expansion of the j-function have any prime coefficients? A superabundance of congruences involving primes up to 13 rule out many candidates, but calculation suggests t …

The following series evaluation $\sum \frac{n^2-1}{(n^2+1)^2}=\frac{1}{2}(1-\frac{\pi^2}{\sinh(\pi)^2})$ seems attractive to me, and has a proof related to the evaluation of $\zeta(2)$. Does this i …

I previously asked generally what people knew or conjectured concerning the moments of the probability distribution governing $M_n:= g_n/\ln(p_n)$, the normalized $n$th prime gap (or ``merit''). Greg …

This showed up in my snail-mail today, so I'm sharing the wealth: http://ifile.it/rodc5is/mazur.pdf