Day 12: Rotating Tables!

Number Theory Level 5

A table with length \(a\), width \(b\) is small if it can be fully rotated in a room with dimensions \(a + 2\), \(b + 2\) (height is discounted).

Find the number of distinct small tables with (positive) integer side lengths.

Note: Rotations and reflections are considered identical.

This problem is part of the set Advent Calendar 2014.

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