Question Number 50383 by prof Abdo imad last updated on 16/Dec/18
$${let}\:{U}_{{n}} =\left\{\left({x},{y}\right)\in{N}^{\mathrm{2}} /\mathrm{2}{x}+\mathrm{3}{y}={n}\right\} \\ $$$${prove}\:{that}\:{U}_{{n}} ={U}_{{n}−\mathrm{2}} \:+{U}_{{n}−\mathrm{3}} −{U}_{{n}−\mathrm{5}} \\ $$$${for}\:{n}\geqslant\mathrm{5}\:. \\ $$