The problem asks if it is possible to color each of the positive integers either red or blue, so that no Pythagorean triple of integers a, b, c, satisfying
a
2
+
b
2
=
c
2
{\displaystyle a^{2}+b^{2}=c^{2}} are all the same color.
For example, in the Pythagorean triple 3, 4 and 5 (
3
2
+
4
2
=
5
2
{\displaystyle 3^{2}+4^{2}=5^{2}}), if 3 and 4 are colored red, then 5 must be colored blue.
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