*The author illustrates how certain determinants can be used to motivate students. The determinants in question have terms in artithmetic progressions.*

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*The author describes a convenient method for calculating determinants where all entries on a given diagonal are equal and for some more general situations.*

*A proof without words approach to the geometric-arithmetic mean inequality*

*Many calculations in number theory have different rules for different residue class mod an integer \(r\). The author shows how to combine these cases using a single amalgamated formula.*...

*The author generalizes the test of convergence for the series involving iterated logarithms from base \(e\) to any positive base.*