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The article focuses on the number theory of Gaussian integers. Within the complex numbers, the analogues of the integers are the Gaussian integers, those complex numbers whose real and imaginary parts are both integers. There is a theory of divisibility, including greatest common divisors, and the purpose of this article is to present a new gcd algorithm for Gaussian integers. The standard algorithm is a straightforward extension of the Euclidean algorithm for ordinary integers. The gcd algorithm is better suited to paper-and-pencil computation, and it is less error-susceptible than the standard one. Another attractive feature is that it is based on a simple parity argument. The basic divisibility definitions for Gaussian integers are simply restatements of those for ordinary integers. There are many interesting results which can be proved using parity arguments. The gcd algorithm establishes that any two Gaussian integers have a greatest common divisor, and it is interesting to see that this result has an odd-even proof.

A review of the article "Why Is Paper-and-Pencil Multiplication Difficult for Many People?" by Robert Speiser, Matthew H. Schneps, Amanda Heffner-Wong, Jaimie L. Miller, and Gerhard Sonnert, that appeared in December 2012 issue of the journal "The Journal of Mathematical Behavior", is presented.

The article presents information on the properties of Graeco-Latin squares enumerated by mathematician Leonhard Euler. Euler suggested that a Graeco-Latin square of size n could never exist for any n of the form 4k +2, although he was not able to prove it. A Latin square is an n-by-n array of n distinct symbols in which each symbol appears exactly once in each row and column. On the other hand a Graeco-Latin square is an n-by-n array of ordered pairs from a set of n symbols such that in each row and each column of the array, each symbol appears exactly once in each coordinate. In one of his papers on Graeco-Latin squares, Euler used magic squares, which are closely related to Graeco-Latin squares. Magic squares were constructed by using Graeco-Latin squares of orders 3, 4 and 5. He showed that a Graeco-Latin square of order n can be converted into a magic square by the use of an algorithm. One can construct Graeco-Latin squares of every order n except those values for which the prime factorization of n contains only a single factor of 2.