There are an infinite number of points with positive coordinates ( $$\(x, y\)$$ ) the sum of whose coordinates is the square of an integer. Among all such points $$\((x, y)\)$$ which one satisfies $$\(y=2 x\)$$ and has $$\(x\)$$ as small as possible?
A.
\(\left(\frac{1}{9}, \frac{2}{9}\right)\)
B.
\(\left(\frac{1}{4}, \frac{1}{2}\right)\)
C.
\((1,2)\)
D.
\(\left(\frac{1}{3}, \frac{2}{3}\right)\)
Exam No：2018 First Round Grades 10-12 Year：2018 Question No：3
Answer:
D
Knowledge points:
G10-12 - Number Theory - Diophantine Equations
Solution:
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