*The author characterizes the positive integers that are the products of two pairs of factors such that the sum of one pair equals the difference of the other.*

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*This is a student research project on zero-divisor graphs of commutative rings, using results from recent professional publications.*

*Inspired by the Pascal triangle, three young "rascals" from three different countries devise a number triangle based on a diamond recurrence formula.*

*The author proves visually the double angle formulas for sine and cosine.*

*How a Saari representation triangle determines the winner of a three-party election for several voting methods is illustrated.*

*The authors prove a necessary and sufficient condition for the existence of the limits of a class of multivariable rational functions commonly seen in textbooks.*

*The author uses the Lambert W function to express the equilibrium solutions of the SIR epidemic model.*

*Following his senior seminars, the author discusses Fermat's last theorem for rational and irrational exponents, in which the rational solutions are characterized.*

*The author provides a characterization of* \(n\)-*dimensional quadratic functions in terms of tangent planes.*