منابع مشابه
Computing small solutions of unit equations in three variables I: Application to norm form equations
We construct an algorithm to enumerate small solutions of unit equations in three variables. The algorithm is a generalization of K.Wildanger’s method [17] and of the method of I.Gaál and M.Pohst [6], and is based on the method of U.Fincke and M.Pohst [4] enumerating lattice points in ellipsoids (see also I.Gaál [5]). We will call a solution small if it has ”small” exponents corresponding to a ...
متن کاملParameterized norm form equations with arithmetic progressions
Buchmann and Pethő [5] observed that following algebraic integer 10 + 9α + 8α + 7α + 6α + 5α + 4α, with α = 3 is a unit. Since the coefficients form an arithmetic progressions they have found a solution to the Diophantine equation (1) NK/Q(x0 + αx1 + · · ·+ x6α) = ±1, such that (x0, . . . , x6) ∈ Z is an arithmetic progression. Recently Bérczes and Pethő [3] considered the Diophantine equation ...
متن کاملNorm Form Equations and Continued Fractions
We consider the Diophantine equation of the form x2−Dy2 = c, where c ∣∣ 2D, gcd(x, y) = 1, and provide criteria for solutions in terms of congruence conditions on the fundamental solution of the Pell Equation x2 − Dy2 = 1. The proofs are elementary, using only basic properties of simple continued fractions. The results generalize various criteria for such solutions, and expose the central norm,...
متن کاملOn the number of solutions of norm form equations
A norm form is a form F(X" ... ,Xn ) with rational coefficients which factors into linear forms over C but is irreducible or a power of an irreducible form over Q. It is known that a nondegenerate norm form equation F(x" .... xn) = m has only finitely many. solutions (XI, .... Xn) E zn. We derive explicit bounds for the number of solutions. When F has coefficients in Z. these bounds depend only...
متن کاملA one-way function based on norm form equations
In this paper we present a new one-way function with collision resistance. The security of this function is based on the difficulty of solving a norm form equation. We prove that this function is collision resistant, so it can be used as a one-way hash function. We show that this construction probably provides a family of one-way functions.
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 1986
ISSN: 0022-314X
DOI: 10.1016/0022-314x(86)90069-7