a= [tex](n^{4}+ 2n^{3}+ n^{2})+( n^{4}+ n^{2}+1+2n^{3}+2n+ 2n^{2} ) [/tex] +[tex] (n^{4}+ 2n^{3}- n^{2}+1) [/tex]
Prima paranteza este egala cu (n²+n)², a doua cu (n²+n+1)², iar a treia cu (n²+n-1)². (se verifica prin calcul).
Asadar a= (n²+n-1)²+(n²+n)²+(n²+n+1)². (suma de patrate a 3 numere consecutive)
