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Let $G$ be a free product of two groups with amalgamated subgroup, $π$ be either the set of all prime numbers or the one-element set \{$p$\} for some prime number $p$. Denote by $Σ$ the family of all cyclic subgroups of group $G$, which are separ...
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We present a characterization of the finite groups in which all real classes have prime powers size....
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In this article, we investigate how Euler might have been led to conjecture the Prime Number Theorem, based on what he knew. We also speculate on why he did not do so....
The prime-counting function $π(x)$ which computes the number of primes smaller or equal to a given real number has a long-standing interest in number theory. The present manuscript proposes a method to compute $π(x)$ with time complexity $\mathcal{...
We show that an elation generalised quadrangle which has p+1 lines on each point, for some prime p, is classical or arises from a flock of a quadratic cone (i.e., is a flock quadrangle)....
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In 1878 É. Lucas proved a remarkable result which provides a simple way to compute the binomial coefficient ${n\choose m}$ modulo a prime $p$ in terms of the binomial coefficients of the base-$p$ digits of $n$ and $m$: {\it If $p$ is a prime, $n=n_0...
Let p be a prime and F a totally real field in which p is unramified. We consider mod p Hilbert modular forms for F, defined as sections of automorphic line bundles on Hilbert modular varieties of level prime to p in characteristic p. For a mod p Hil...
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6 days ago · Here are all the new releases and everything coming to Amazon Prime Video in February, including Cross Season 2, the erotic thriller 56 Days, and the action movie The Bluff.