A classical result of Euler states that the tangent numbers are an alternating sum of Eulerian numbers. A dual result of Roselle states that the secant numbers can be obtained by a...
We look at binary strings of length n which contain no odd run of zeros and express the total number of such strings, the number of zeros, the number of ones, the total number of ...
This paper deals with products of moderate-size primes, familiarly known as smooth numbers. Smooth numbers play an crucial role in information theory, signal processing and crypto...
We design new feed-forward multi-layered neural networks which perform di erent elementary arithmetic operations, such as bit shifting, addition of N p-bit numbers, and multiplica...
An analogue for composite moduli m ≥ 2 of the Wilson quotient is studied. Various congruences are derived, and the question of when these quotients are divisible by m is investig...