a. \(25-y^2=8\left(x-2009\right)\)
\(\Leftrightarrow25-y^2=8x-16072\)
\(\Leftrightarrow25-y^2+16072=8x\)
\(\Leftrightarrow16097-y^2=8x\)
\(\Leftrightarrow\dfrac{16097-y^2}{8}=x\)
\(\Leftrightarrow\dfrac{16096+1-y^2}{8}=x\)
\(\Leftrightarrow2012+\dfrac{1-y^2}{8}=x\)
-Vì \(x,y\) nguyên \(\Rightarrow\left(1-y^2\right)⋮8\)
\(\Leftrightarrow\left(1-y\right)\left(y+1\right)⋮8\)
\(\Leftrightarrow\left(1-y\right)⋮8\) hay \(\left(y+1\right)⋮8\)
\(\Leftrightarrow\left(1-y\right)\in\left\{1;2;4;8;-1;-2;-4;-8\right\}\) hay \(\left(y+1\right)\in\left\{1;2;4;8;-1;-2;-4;-8\right\}\)
\(\Leftrightarrow y\in\left\{0;-1;-3;-7;2;3;5;9\right\}\) hay \(y\in\left\{0;1;3;7;-2;-3;-5;-9\right\}\)
\(\Rightarrow y\in\left\{0;\pm1;\pm2;\pm3;\pm5;\pm7;\pm9\right\}\)
-Từ đó bạn tính các giá trị x tương ứng với mỗi giá trị của y.
