This paper presents two algorithms using the Newton-Raphson method to calculate the floor of y**(1/m) for natural integer numbers y > 2 and m > 1, which can be used to determine if y is an integer pow…

This paper introduces the concept of 'large' zeros in linear recurrence sequences and establishes that they either do not exist or are very sparse, which could lead to decidability of the Skolem Probl…

This paper provides bounds on the difference between the annihilation number and independence number of a finite simple graph, and proves these bounds for various types of graphs.

This paper traces the historical development of the square-and-multiply algorithm, arguing that while its conceptual foundation dates back to ancient Indian prosody, its formal articulation as a gener…

This paper introduces new algorithms for finding prime numbers up to a given bound, achieving a speedup of log N over the sieve of Eratosthenes.

The paper establishes bijections between tree records, girth of connected endofunctions, and genesis sequences, deriving generating functions for tree and forest record numbers using Cayley's tree fun…

The paper studies properties of parity based bit-counting complexity classes B|0|⊕P and B|1|⊕P, proves inclusions and closures, and shows they contain PH and are contained in CH.

This paper provides the first unconditional proof for Weber's Conjecture for the case $k ext{ up to } 12$, which is crucial for lattice-based cryptography.

This paper shows #P-completeness for several graph counting problems using a new technique.

The paper studies the affine family of signings for a d-regular graph and shows that averaging over it converts the sign problem of the Bilu-Linial conjecture into a counting problem, proving matched…

This paper introduces a symbolic diagnostic approach for investigating obstruction structures in the Collatz conjecture using finite exponent codes of the accelerated map.

This paper presents methods for ranking and unranking permutations avoiding a pattern of length three in lexicographic or colexicographic order.

This paper proves DP-completeness of Exact-3-DNP and Exact-4-DNP by reducing 3SAT to these problems.

This paper derives multivariate generating functions to refine the enumeration of Fibonacci polyominoes.

This paper investigates the closeness of singularity for $n imes n$ unimodular matrices, specifically for $(2k+1)$-ary and $(k+1)$-ary cases of $4 imes 4$ nonnegative unimodular matrices.