E.374. Determinați numărul natural nnn pentru care 2n+1⋅5n+2+2n⋅5n+1+2n+2⋅5n=590.2^{n+1} \cdot 5 ^{n+2} + 2^n \cdot 5 ^{n+1} + 2^{n+2} \cdot 5^n=590.2n+1⋅5n+2+2n⋅5n+1+2n+2⋅5n=590.
Răspuns: n=1.n=1.n=1.