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Grade Vs Difficulty:

This lesson has a handout that describes some facts related to the Euclidean Algorithm together with some related problems. There is also a second handout that just contains some problems. The Euclidean algorithm is an important part of the Rational Tangle activity.
There is a second activity in the lesson plan section that has even more difficult questions related to the Euclidean algorithm and the ABC conjecture. See
Number theory and ABC.