منابع مشابه
The Distribution of Squarefull Numbers in Short Intervals
It follows that there is a positive constant c1 and arbitrarily large values of x for which the interval (x; x+ c1x ] contains no squarefull numbers. On the other hand, since there is a square in (x; x + 2 p x + 1] for all x 0, it follows that there is a constant c2 such that for every x 1, the interval (x; x + c2x] contains a squarefull number. Thus, the order of the maximum size of gaps betwe...
متن کاملTribonacci Numbers with Indices in Arithmetic Progression and Their Sums
In this paper, we give a recurrence relation for the Tribonacci numbers with indices in aritmetics progression, fTrnCsg for 0 s < n. We find sums of fTrng for arbitrary integer r via matrix methods. 2000 Mathematics Subject Classification: 11B39; 11C20
متن کاملAnti-van der Waerden Numbers of 3-Term Arithmetic Progression
The anti-van der Waerden number, denoted by aw([n], k), is the smallest r such that every exact r-coloring of [n] contains a rainbow k-term arithmetic progression. Butler et al. showed that dlog3 ne + 2 6 aw([n], 3) 6 dlog2 ne + 1, and conjectured that there exists a constant C such that aw([n], 3) 6 dlog3 ne + C. In this paper, we show this conjecture is true by determining aw([n], 3) for all ...
متن کاملPrimes in arithmetic progression
Prime numbers have fascinated people since ancient times. Since the last century, their study has acquired importance also on account of the crucial role played by them in cryptography and other related areas. One of the problems about primes which has intrigued mathematicians is whether it is possible to have long strings of primes with the successive primes differing by a fixed number, namely...
متن کاملPalindromic Numbers in Arithmetic Progressions
Integers have many interesting properties. In this paper it will be shown that, for an arbitrary nonconstant arithmetic progression {an}TM=l of positive integers (denoted by N), either {an}TM=l contains infinitely many palindromic numbers or else 10|aw for every n GN. (This result is a generalization of the theorem concerning the existence of palindromic multiples, cf. [2].) More generally, for...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2015
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2014.12.019