[tex]\displaystyle\\
\text{Problema cere sa scriem numarul }35^{2017} \text{ ca suma de cuburi perfecte.}\\\\
35^{2017}=\\
=35^{2016+1} =\\
=35^{2016}\times35^1=\\
=35^{2016}\times35=\\
=35^{2016} \times (8+27) =\\
=35^{672\times3}\times(8+27)=\\
=\Big(35^{672}\Big)^3}\times(2^3+3^3)=\\
=\Big(35^{672}\Big)^3}\times2^3+\Big(35^{672}\Big)^3}\times 3^3=\\
=\boxed{\Big(2\times35^{672}\Big)^3+\Big(3\times35^{672}\Big)^3}\\\\
\text{Raspuns:}\\\\
a=\boxed{2\times35^{672}}\\
b=\boxed{3\times35^{672}}
[/tex]
