Color each positive integer with red and blue, whether there must be three numbers $a, b, c$ with same color such that $a^2+b^2 = c^2$?

Question

Color each positive integer with red and blue, whether there must be three numbers $a, b, c$ with same color such that $a^2+b^2 = c^2$? Such as if $3,4,5$ is blue, then $3^2 + 4^2 = 5^2$. Is there a color scheme so that there are no such three numbers?