# Equal Modulusly?

Algebra Level 2

True or False?

For positive integers $$x, y,$$ and $$n,$$ $x \times ( y \bmod n) = y \times ( x \bmod n ).$

Note: The notation $$(a \bmod n )$$ refers to the remainder when $$a$$ is divided by $$n$$. It is between 0 and $$n -1$$ inclusive.


Bonus:

• What if we extend to real numbers $$x, y,$$ and $$n$$?
• What does this imply about complex exponentiation?
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