BADIDJA, Salim2018-03-142018-03-142018-02-01http://dspace.univ-msila.dz:8080//xmlui/handle/123456789/3623The representation of a positive integer N by a sum of elements of agiven sequence Is an interesting problem which is wellknown in the mathematical literature, namely the Unique representation as a sum of distinct Lucas numbers(Brown,Jr,1969),Fibonacci and Lucas representation (Pihko,1986),Cantor’s development(Mercier,2004),....In addition, In the framework of the non standard analysis, A. Boudaoud proposed another method of representation of N; It is to write it according to the following model:en