منابع مشابه
Diophantine approximation and Diophantine equations
The first course is devoted to the basic setup of Diophantine approximation: we start with rational approximation to a single real number. Firstly, positive results tell us that a real number x has “good” rational approximation p/q, where “good” is when one compares |x − p/q| and q. We discuss Dirichlet’s result in 1842 (see [6] Course N◦2 §2.1) and the Markoff–Lagrange spectrum ([6] Course N◦1...
متن کاملSolvability of Diophantine Equations
Attila Bérczes (University of Debrecen): On arithmetic properties of solutions of norm form equations. Abstract. Let α be an algebraic number of degree n and K := Q(α). Consider the norm form equation NK/Q(x0 + x1α+ x2α + . . .+ xn−1α) = b in x0, . . . , xn−1 ∈ Z. (1) Let H denote the solution set of (1). Arranging the elements of H in an |H| × n array H, one may ask at least two natural questi...
متن کاملComplete decomposition of Dickson-type polynomials and related Diophantine equations
We characterize decomposition over C of polynomials f (a,B) n (x) defined by the generalized Dickson-type recursive relation (n ≥ 1), f (a,B) 0 (x) = B, f (a,B) 1 (x) = x, f (a,B) n+1 (x) = xf (a,B) n (x)− af (a,B) n−1 (x), where B, a ∈ Q or R. As a direct application of the uniform decomposition result, we fully settle the finiteness problem for the Diophantine equation f (a,B) n (x) = f (â,B̂)...
متن کاملFamilies of Diophantine equations
This is a report on the recent work by Claude Levesque and the author on families of Diophantine equations. This joint work started in 2010 in Rio, and this is still work in progress. The lecture in Lahore on March 11, 2013 was mainly devoted to a survey of results on Diophantine equations, with the last part dealing with some recent results. Here we describe the content of the recent joint pap...
متن کاملOn Two Diophantine Equations of Ramanujan-nagell Type
In this paper, we prove two conjectures of Ulas ([21]) on two Diophantine equations of Ramanujan-Nagell type. In fact, we show that the following equations x + (2 + 1)2 = 2 + 2 + 2 + 2 + 1, x + 1 3 ( 2 − 1 ) 2 = 1 9 ( 49 · 4 − 11 · 4 + 1 ) have exactly four solutions.
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 1996
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700017007