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Littlewood [17] stated "Try a hard problem. You may not solve it, but you will solve something else". In this paper, we concentrate on six of the most famous and important unsolved problems in Mathematics. For each such problem we offer two suggestions to try to solve it. Even though some of these suggestions have been tried by the author with interesting results, he hopes that others will have more success thus attaining the objective of advancing knowledge. Our first problem begins with (clear) prime numbers while our last problem concludes with (hidden) prime numbers (Read on to discover the difference). [ABSTRACT FROM AUTHOR]

In this paper, we establish and prove some common fixed points for self-maps in a complete cone metric space that generalize and improve earlier results in the literature. [ABSTRACT FROM AUTHOR]

In ring theory, many significant studies have raised connections between the derivations and the structures of rings. Derivations of rings developed gradually more than half a century ago. In particular, the generalizations of the derivation concept play an important role in the calculation of the eigenvalues of matrices, which is important in mathematics and other sciences, business, engineering, and quantum physics. The main goal of this article is to introduce identities in prime and semiprime rings concerning left multiplicative centralizers and multiplicative (generalized)-derivations that have descriptions of these mappings. Some properties of the proposed identities are proven, and the relationships between these identities in terms of the notions of the multiplicative (generalized)-derivation (MG-D) and the multiplicative left centralizer (MLC) for an associative ring S are studied. If the condition ζ(κ1κ2)±[τ (κ1), κ2]±κ1κ2 = 0 is held for all κ1 and κ2 in an ideal J (6= 0) of S, then either ζ is an MLC on S or S is commutative. Furthermore, examples are given to show that semiprimeness and primeness are irreplaceable conditions. [ABSTRACT FROM AUTHOR]

In this article we decided to begin with the 12th Century because this century witnessed huge mathematical interest in Western Europe stimulated by Arabic original books as well as translated ones being translated into Latin (which became the venue of intellectual and scientific domains in Western Europe and remained in this academic function until the 18th century) at Spain translation centers. Despite the long war between the kingdoms of England and France from 1337 to 1453 resulting in famine and plague in the 14th and the first half of the 15th century, the year 1450 witnessed the advent of the printing press which had an enormous impact on printing arithmetic books for the purpose of teaching business people computational methods for their commercial needs. A more detailed treatment is done on later centuries. [ABSTRACT FROM AUTHOR]

Let G be a forest with n edges. El-Zanati conjectures that G necessarily decomposes every 2n-regular graph and every n-regular bipartite graph. We confirm these conjectures in the case when G consists of two stars. [ABSTRACT FROM AUTHOR]

Let u ≠ ±1, v² be a fixed integer, let p be a prime number, and let ordp(u) = d|p - 1 be the order of u mod p. This note provides a lower bound #{p ≤ x : ordp(u) = p-1} ≫ x(log x)-1 for the number of primes p ≤ x with a fixed primitive root u mod p for all large numbers x ≥ 1. The current results in the literature have the lower bound #{p ≤ x : ordp(u) = p - 1} ≫ x(log x)-2, and restrictions on the fixed primitive root to a subset of at least three or more integers. [ABSTRACT FROM AUTHOR]