Displaying similar documents to “Operations of Points on Elliptic Curve in Projective Coordinates”

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.

Proth Numbers

Christoph Schwarzweller (2014)

Formalized Mathematics

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In this article we introduce Proth numbers and prove two theorems on such numbers being prime [3]. We also give revised versions of Pocklington’s theorem and of the Legendre symbol. Finally, we prove Pepin’s theorem and that the fifth Fermat number is not prime.

On a family of elliptic curves.

Antoniewicz, Anna (2005)

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica

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A note on a conjecture of Jeśmanowicz

Moujie Deng, G. Cohen (2000)

Colloquium Mathematicae

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Let a, b, c be relatively prime positive integers such that a 2 + b 2 = c 2 . Jeśmanowicz conjectured in 1956 that for any given positive integer n the only solution of ( a n ) x + ( b n ) y = ( c n ) z in positive integers is x=y=z=2. If n=1, then, equivalently, the equation ( u 2 - v 2 ) x + ( 2 u v ) y = ( u 2 + v 2 ) z , for integers u>v>0, has only the solution x=y=z=2. We prove that this is the case when one of u, v has no prime factor of the form 4l+1 and certain congruence and inequality conditions on u, v are satisfied.

Lagrange’s Four-Square Theorem

Yasushige Watase (2014)

Formalized Mathematics

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This article provides a formalized proof of the so-called “the four-square theorem”, namely any natural number can be expressed by a sum of four squares, which was proved by Lagrange in 1770. An informal proof of the theorem can be found in the number theory literature, e.g. in [14], [1] or [23]. This theorem is item #19 from the “Formalizing 100 Theorems” list maintained by Freek Wiedijk at http://www.cs.ru.nl/F.Wiedijk/100/.