The least common multiple of consecutive arithmetic progression terms
نویسندگان
چکیده
منابع مشابه
Powers from Products of Consecutive Terms in Arithmetic Progression
A celebrated theorem of Erdős and Selfridge [14] states that the product of consecutive positive integers is never a perfect power. A more recent and equally appealing result is one of Darmon and Merel [11] who proved an old conjecture of Dénes to the effect that there do not exist three consecutive nth powers in arithmetic progression, provided n 3. One common generalization of these problems ...
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In 1967 the first set of 6 consecutive primes in arithmetic progression was found. In 1995 the first set of 7 consecutive primes in arithmetic progression was found. Between November, 1997 and March, 1998, we succeeded in finding sets of 8, 9 and 10 consecutive primes in arithmetic progression. This was made possible because of the increase in computer capability and availability, and the abili...
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It is conjectured that there exist arbitrarily long sequences of consecutive primes in arithmetic progression. In 1967, the first such sequence of 6 consecutive primes in arithmetic progression was found. Searching for 7 consecutive primes in arithmetic progression is difficult because it is necessary that a prescribed set of at least 1254 numbers between the first and last prime all be composi...
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has only the solution (n, k, b, y, l) = (48, 3, 6, 140, 2) in positive integers n, k, b, y and l, where k, l ≥ 2, P (b) ≤ k and P (y) > k. Here, P (m) denotes the greatest prime factor of the integer m (where, for completeness, we write P (±1) = 1 and P (0) = ∞). Rather surprisingly, no similar conclusion is available for the frequently studied generalization of this equation to products of con...
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Let nr(a,q) be the least /--free number in the arithmetic progession a modulo q. Several results are proved that give lower bounds for n,.(a, q), improving on previous results due to Erdös and Warlimont. In addition, a heuristic argument is given, leading to two conjectures that would imply that the results of the paper are close to best possible.
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ژورنال
عنوان ژورنال: Proceedings of the Edinburgh Mathematical Society
سال: 2011
ISSN: 0013-0915,1464-3839
DOI: 10.1017/s0013091509000431