Equal Modulusly?

Algebra Level 2

True or False?

For positive integers x,y,x, y, and n,n, x×(ymodn)=y×(xmodn). x \times ( y \bmod n) = y \times ( x \bmod n ).

Note: The notation (amodn) (a \bmod n ) refers to the remainder when aa is divided by n n . It is between 0 and n1 n -1 inclusive.


Bonus:

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