Displaying similar documents to “On Square-Free Numbers”

More on Divisibility Criteria for Selected Primes

Adam Naumowicz, Radosław Piliszek (2013)

Formalized Mathematics

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This paper is a continuation of [19], where the divisibility criteria for initial prime numbers based on their representation in the decimal system were formalized. In the current paper we consider all primes up to 101 to demonstrate the method presented in [7].

Set of Points on Elliptic Curve in Projective Coordinates

Yuichi Futa, Hiroyuki Okazaki, Yasunari Shidama (2011)

Formalized Mathematics

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In this article, we formalize a set of points on an elliptic curve over GF(p). Elliptic curve cryptography [10], whose security is based on a difficulty of discrete logarithm problem of elliptic curves, is important for information security.

Wilson’s theorem

Chandan Singh Dalawat (2009)

Journal de Théorie des Nombres de Bordeaux

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We show how K. Hensel could have extended Wilson’s theorem from Z to the ring of integers 𝔬 in a number field, to find the product of all invertible elements of a finite quotient of 𝔬 .

Isomorphisms of Direct Products of Finite Commutative Groups

Hiroyuki Okazaki, Hiroshi Yamazaki, Yasunari Shidama (2013)

Formalized Mathematics

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We have been working on the formalization of groups. In [1], we encoded some theorems concerning the product of cyclic groups. In this article, we present the generalized formalization of [1]. First, we show that every finite commutative group which order is composite number is isomorphic to a direct product of finite commutative groups which orders are relatively prime. Next, we describe finite direct products of finite commutative groups