O pewnej implikacji

The purpose of this paper is to show how the process of provinga theorem in different ways or proving generalized versions of the theorem,after learning one its proofs, influences the development of the skills of provingtheorems and analysing proofs by the students of mathematics. Toillustrate this process we use an elementary theorem about numbers and itsgeneralizations, giving fourteen proofs. Proving theorems we use methodsand facts which are available to high school students.