When a function in arithmetic modulo n is represented through a cartesian graph, the resulting set of points reveals little information about the form of the function (for example, see Fig. 1). It is not easy to discern connections between the points; a restriction to the values 0, 1, 2,…, n — 1 would have to be placed on x and y; and the fact that n — 1 is as ‘near’ to 0 as 1 is, is not apparent in the graph.

Algebraic magic squares of order 4, constructed with the numbers 1, 2,… 16, are of three main types.

From the 4 × 4 frame, nine 2 × 2 quadrants may be cut, and the sum of the numbers in these quadrants furnishes the criteria for distinguishing between the various types of magic squares.

For a long time prime numbers have attracted the attention of mathematicians, especially those primes that possess some sort of a symmetry. The mysterious repunits An = 111… 1(n), whose decimal representations contain only units, form an important class of them. For a repunit to be prime the number n of its digits must be also prime. But this condition is far from being sufficient: for instance, A3 = 111 = 3.37 and A5 = 11111 = 41.271. Some of the repunits are nonetheless prime: A2, A19, A23, A317 and A1031, are the only known examples. The question of primeness of the repunits was discussed by M. Gardner and later in [2–4]. It is not clear whether the number of prime repunits is finite or infinite.