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An Information Theoretic Condition for Perfect Reconstruction. [PDF]

Entropy (Basel)
Delsol I, Rioul O, Béguinot J, Rabiet V, Souloumiac A.   +4 more
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Sylow p-groups of polynomial permutations on the integers mod [Formula: see text].

J Number Theory, 2013
Frisch S, Krenn D.
europepmc   +1 more source

Étale neighbourhoods and the normal crossings locus.

Expo Math, 2011
Bruschek C, Wagner D.
europepmc   +1 more source

Last nonzero digits and p-adic valuations of special sequences

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p-adic valuation of exponential sums associated to trinomials and some consequences

p-Adic Numbers, Ultrametric Analysis and Applications, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Castro, Francis N., Figueroa, Raúl
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p-adic Valuation of the Sum of Divisors

Frontiers of Mathematics
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhao, Junjia, Chen, Yonggao
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p-Adic Valuation of Euler’s Totient Function

Bulletin of the Malaysian Mathematical Sciences Society
Let \(\phi(n)\) be the Euler phi function. The paper proves theorems about what powers of primes can divide \(\phi(n)\) and how large those prime powers can be. Let \(v_p(n)\) be the largest number \(k\) such that \(p^k|n\). Then they note that trivially one has that \(v_2(\phi(n)) \leq \lfloor \log_2 n\rfloor\).
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The p-adic valuations and degrees of monomial exponential sums

The Ramanujan Journal
In this paper, the authors study the \(p\)-adic valuations and the algebraic degrees of the Gauss sum \(S_k(x^d)\) over \(\mathbb{F}_{p^k}\), which is defined by \begin{align*} S_k(x^d)=\sum_{x\in \mathbb{F}_{p^k}}\zeta_p^{\operatorname{Tr}_k(x^d)}. \end{align*} From the local perspective, one can view the Gauss sum \(S_k(x^d)\) as a \(p\)-adic number.
Yang, Liping, Deng, Xiantao
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The p -Adic Valuation of Lucas Sequences

The Fibonacci Quarterly, 2016
Let (un)n≥0 be a nondegenerate Lucas sequence with characteristic polynomial X2 − aX − b, for some relatively prime integers a and b. For each prime number p and each positive integer n, we give simple formulas for the p-adic valuation νp(un), in terms of νp(n) and the rank of apparition of p in (un)n≥0. This generalizes a previous result of Lengyel on
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