Question

determinati numerele naturale de forma ab stiind ca suma dintre ab si ba este patrat perfect

Answer 1

[tex]\overline{ab}=10a+b\\ \overline{ba}=10b+a\\ \overline{ab}+\overline{ba}=10a+b+10b+a=11a+11b=11(a+b)\\ \text{Pentru ca $11(a+b)$ sa fie patrat perfect, tinand seama ca $a+b\leq18$}\\ \text{este necesar si suficient ca $a+b=11$.}\\ \text{Asadar, obtinem numerele care indeplinesc conditia data: }\\ 29,38,47,56,65,74,83,92. [/tex]