Almost squares in arithmetic progression (III)
نویسندگان
چکیده
منابع مشابه
On 4 Squares in Arithmetic Progression
x1 − 2x2 + x3 = 0 x2 − 2x3 + x4 = 0 are given by (x1, x2, x3, x4) = (±1,±1,±1,±1). Now, the above variety is an intersection between 2 quadrics in P. In general – i.e., except for the possibility of the variety being reducible or singular – an intersection between 2 quadrics in P is (isomorphic to) an elliptic curve and there is an algorithm that brings the curve to Weierstraß form by means of ...
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We give several criteria to show over which quadratic number fields Q( √ D) there should exists a non-constant arithmetic progressions of five squares. This is done by translating the problem to determining when some genus five curves CD defined over Q have rational points, and then using a Mordell-Weil sieve argument among others. Using a elliptic Chabauty-like method, we prove that the only n...
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An almost square of type 2 is an integer n that can be factored in two different ways as n = a1b1 = a2b2 with a1, a2, b1, b2 ≈ √ n. In this paper, we shall improve upon our previous results on short intervals containing such an almost square. This leads to another question of independent interest: given some 0 < c < 1, find a short interval around x which contains an integer divisible by some i...
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ژورنال
عنوان ژورنال: Indagationes Mathematicae
سال: 2004
ISSN: 0019-3577
DOI: 10.1016/s0019-3577(04)80016-8