This is my newest problem, to appear in the October 2010 issue of La Voz.

What is this picture asking? Ben suggested that instead of bold black squares, I should have indicated the squares with something especially significant to grasshoppers. Something tasty or something dangerous?

Where did this come from? This problem is related to a derivation of the formula for Primitive Pythagorean Triples: Find all relatively prime natural number triples (a,b,c) that satisfy the equation

The first step in my favorite elementary number theory proof is to show that not both a and b are odd. This would imply that c is one of the shaded squares above: 2, 6, 10, 14, …

Does the grasshopper land on a (boxed) square?

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