Có bao nhiêu cặp số nguyên (x; y) thoả mãn $0<y<2020$ và...

Ta có:

f\left( t \right)={{3}^{t}}+t{f}'\left( t \right)=1+{{3}^{t}}.\ln 3>0, \forall tf\left( t \right)\mathbb{R}\Leftrightarrow f\left( x-1 \right)=f\left( {{\log }_{3}}\left( 3y \right) \right)\Leftrightarrow x-1={{\log }_{3}}\left( 3y \right)\Leftrightarrow x-2={{\log }_{3}}y\Leftrightarrow y={{3}^{x-2}}y\in \left( 0;2020 \right){{3}^{x-2}}<2020\Leftrightarrow x-2<{{\log }_{3}}2020\Leftrightarrow x<2+{{\log }_{3}}2020x;y\in \mathbb{Z}x\in \left\{ 2;3;4;5;6;7;8 \right\}xy7$ cặp số nguyên (x; y) thoả mãn yêu cầu bài toán.