A generalization of the Subbarao identity.
A geometric method for the approximation by nearest integer continued fractions. (Eine geometrische Methode bei der Approximation durch Kettenbrüche nach dem nächsten Ganzen.)
A geometric proof of Kummer's reciprocity law for seventh powers
A Goldbach theorem for polynomials of low degree over odd finite fields
A Good Basis for Computing with Complex Numbers.
A localization theorem in the theory of diophantine approximation and an application to Pell's equation
A logical alternative to the existing positional number system.
A Markov approach to the generalized Syracuse algorithm
A matrix inequality for Möbius functions.
A Menon-type identity using Klee's function
Menon’s identity is a classical identity involving gcd sums and the Euler totient function . A natural generalization of is the Klee’s function . We derive a Menon-type identity using Klee’s function and a generalization of the gcd function. This identity generalizes an identity given by Y. Li and D. Kim (2017).
A million new amicable pairs.
A multivariate arithmetic function of combinatorial and topological significance.
A natural prime-generating recurrence.
A necessary and sufficient condition for the primality of Fermat numbers
We examine primitive roots modulo the Fermat number . We show that an odd integer is a Fermat prime if and only if the set of primitive roots modulo is equal to the set of quadratic non-residues modulo . This result is extended to primitive roots modulo twice a Fermat number.
A negative answer to two questions about the smallest prime numbers having given digital sums.
A new class of continued fraction expansions
A New Condition for Consecutive Primitive Roots of a Prime.
A new Fibonacci-like sequence of composite numbers.
A new formulation of the law of octic reciprocity for primes =+-3 (mod 8) and its consequences.
A New Infinite Product Representation for Real Numbers.