Found a tight pre-period bound on "Counting Sequences" (i.e. Inventory sequences, Think-and-say sequences, or infinite-base Peapod sequences). A variation of the Look-and-say sequence in which digits are counted globally rather than in consecutive runs. Answered a 26 year old open question. arXiv:2004.00209

The co-author "Sela T. Enin" is my wife under the pseudonym of her favorite pokemon,  Ninetales, in reverse.

Demonstrated all perfect powers of 5 can be created from its own base-10 digits along with basic arithmetic and exponentiation. Also demonstrated that the powers of 5 contain arbitrarily long consecutive runs of zeros. arXiv:1910.13829

are multisets whose elements have equal sum and product. Enumerated all such multisets in various domains: integers, fields, rationals, lunar arithmetic, and some quadratic extensions. In all such instances, any composite number can be realized as the sum-proudct of a bioperational multiset, which is not immediately obvious for quadratic extensions, at the least. arXiv:1908.03235

Related the magic square of squares to some factorization problems over the Gaussian integers. Conjectured an enumeration of finite fields in which the magic square of squares is possible. Calculated some surprisingly large rings Z/nZ in which the magic square of squares puzzle is not solvable (i.e. large n for which the puzzle is not solvable modularly). Reviewed on Numberphile for using Matt Parker's name as a new technical term. arXiv:1908.03236