Palestra: On a new procedure to obtain the number of  unrestricted partitions

In this talk we want to present a new correspondence between the number of unrestrited partitions of n and the number of non-negative solutions of systems of two equations, involving natural numbers in the interval (1 ; n2). But to reach this goal we need first to present a procedure described relating unrestricted partitions with paths in the cartesian plane, and partitions of numbers in the interval (1; n2) into distinct odd parts all greater than 1. Then we show that these numbers can also be partitioned into squared parts, and finally present the relation of these partitions with systems of two equations.