5 papers
Polymorphic Numbers with Exponential Prefix
Samer Seraj
We observe that the computation has the digital property of the result being equal to the exponent concatenated directly to the left of the base. The generalization to a…
Diophantine Analysis of a Digital Anomaly
Samer Seraj
The arithmetic-digital anomaly of has been observed several times in the past. We generalize it to an exponential Diophantine equation and inequality in the general num…
Sum of Distinct Biquadratic Residues Modulo Primes
Samer Seraj
Two conjectures, posed by Finch-Smith, Harrington, and Wong in a paper published in Integers in , are proven. Given a monic biquadratic polynomial , we…
Functions with Diffusive Properties
Samer Seraj
While exploring desirable properties of hash functions in cryptography, the author was led to investigate three notions of functions with scattering or "diffusive" properties, wher…
Sum of Cubes is Square of Sum
Edward Barbeau, Samer Seraj
Inspired by the fact that the sum of the cubes of the first naturals is equal to the square of their sum, we explore, for each , the Diophantine equation representing all no…