Exercises in Elementary Number Theory (I)

In this article we propose some exercises on Elementary Number Theory; they don’t require advanced mathematical knowledge. Other articles will follow with exercises related to this beautiful branch of mathematics. We recall that the symbol $$\left\lfloor x \right\rfloor$$ denotes the integer part of the real number $$x$$, i.e. the largest Read more…

Euler’s Polygon Triangulation Problem

Problem Let P be a convex polygon with $$n$$ sides. Calculate in how many different ways the polygon can be divided into triangles using diagonals that do not intersect each other in the interior of P. This problem was proposed by Euler in 1751 to his friend Christian Goldbach. Read more…

Counting Numbers with Adjacent Digits

Problem Suppose we only use the digits of the set $$A = \{1,2,3,4,5 \}$$. How many numbers of $$n$$ digits can be formed with the set $$A$$, if all adjacent digits differ exactly by $$1$$? We denote the number we are looking for with $$a(n)$$. HintIf \(n = Read more…