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More Triangular Number Results, Bruce Brandt

Journal of the Minnesota Academy of Science

I define an increasing function from triangular numbers to triangular numbers and prove it preserves [mathematical symbol]. I conjecture that whether a triangular number is in the image of this function is related to the magnitude of [mathematical symbol] on the triangular number. Parallel theorems and conjectures exist for pentagonal numbers. I also make conjectures about the partial sums of [mathematical symbol] on the triangular numbers along with a conjecture about the sums of absolute values of [mathematical symbol] on the squares.