research
Research and expository work
This page collects one computational replication and one completed expository algebra paper. They are different kinds of work, so each entry states its evidence and its limits separately.
Fibonacci residues modulo prime powers
I counted which residues appear for Fibonacci, Lucas, and Pell sequences modulo prime powers. The Fibonacci computations match selected published benchmark values. The Lucas and Pell observations are finite experiments, not proofs or claims of new discoveries.
read the full studyAlgebraic Properties of Quaternions
Written for a Long Island research program, this paper works through the quaternion group Q8, its Cayley table and center, and the standard conjugate-and-norm formula for inverses in Hamilton's quaternions. It explains established mathematics; it does not claim a new theorem or original result.
read the paper overview and reflectionwhat a reader can inspect
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computational evidence
Pair-state orbit enumeration, recurrence definitions, tests, data, and published benchmarks across 147 finite runs, with 78 direct cross-checks for the Fibonacci study.
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proof-based work
The quaternion page records the definitions, key calculations, main conclusions, and a candid note about the associativity gap I would fix in a revision.
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limits and sources
Both entries separate standard or published results from my own calculations and avoid claiming a new mathematical result.