Perfect powers in products of terms in an arithmetical progression III
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 ...
متن کاملPerfect powers in arithmetic progression 1 PERFECT POWERS IN ARITHMETIC PROGRESSION. A NOTE ON THE INHOMOGENEOUS CASE
We show that the abc conjecture implies that the number of terms of any arithmetic progression consisting of almost perfect ”inhomogeneous” powers is bounded, moreover, if the exponents of the powers are all ≥ 4, then the number of such progressions is finite. We derive a similar statement unconditionally, provided that the exponents of the terms in the progression are bounded from above.
متن کاملOn a sum involving powers of reciprocals of an arithmetical progression
Our purpose is to establish the following result: Let a and d be coprime integers and a, a+ d, a+ 2d, . . . , a+ (k − 1) d (k > 2) be an arithmetical progression. Then for all integers α0, α1, . . . , αk−1 the rational number 1/a0 + 1/ (a + d)α1 + · · · + 1/ (a + (k − 1) d)αk−1 is never an integer. This result extends theorems of Taeisinger (1915) and Kürschák (1918), and also generalizes a res...
متن کاملAlmost Perfect Powers in Consecutive Integers (ii)
Let k 4 be an integer. We find all integers of the form by where l 2 and the greatest prime factor of b is at most k (i.e. nearly a perfect power) such that they are also products of k consecutive integers with two terms omitted.
متن کاملOptimal lot size of EPQ model considering imperfect and defective products
The economic production quantity (EPQ) is a commonly used inventory model. An assumption in the EPQ model is that all units produced are perfect. Some researchers have studied the effects after relaxing this assumption on the inventory models. The objective of this paper is to determine the economic production quantity with reduced pricing, rework and reject situations in a single-stage system ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006