Ismail Hammoudeh

Plane Sections of Symmetric Tetrahedral Cones: Inverse Fibers, Poncelet 3-Porisms, Phase Transitions, and Triangle Loci

We study triangles cut from a one-parameter family of symmetric trihedral cones, equivalently from tetrahedra whose equilateral base is allowed to recede arbitrarily far. Exact elimination reduces the fixed-height inverse problem to a quartic and exposes fold, escape, and parabol...

Reciprocal Periods and Primality: A period-primality toolbox and the rarity of small-index pseudoprimes

Suppose the exact reciprocal period L_b(n) is known for an odd integer n and a base b coprime to n. How much primality information is already contained in that period? This work assembles a period–primality toolbox connecting multiplicative order with Lucas’ criterion, Fermat and...

Reciprocal Periods and Primality: A period-primality toolbox and the rarity of small-index pseudoprimes

Suppose the exact reciprocal period L_b(n) is known for an odd integer n and a base b coprime to n. How much primality information is already contained in that period? This work assembles a period–primality toolbox connecting multiplicative order with Lucas’ criterion, Fermat and...