More fun in 2015, Part 23

Algebra Level 5

How many orthogonal 2 x 2 matrices \(A\) are there such that all the entries of \(2015A\) are integers?

For those who don't know matrices yet, we state the problem (less elegantly) in terms of vectors: How many ordered pairs of perpendicular unit vectors \(v,w\) with two real components are there such that all the components of \(2015v\) and of \(2015w\) are integers?

Hint: Find the Pythagorean triples with 2015 as the hypotenuse.

×

Problem Loading...

Note Loading...

Set Loading...