Question

a^3+b^3=35^2017 Aflati a si b

Answer 1

   
[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]