I would argue the statement 'zero divides zero' is true.
We say '3 divides 6' because there exists an integer solution to the eaquation 3k = 6
experimental evidence suggests there is exactly one solution to the equation ie: k = 2
Similarly 'zero divides zero' is equivalent to the statement there exists an integer solution to the equation 0k = 0.
That there are many solutions for k to this equation (rather than exactly one) is not relevant because of the nature of 'there exists'
My lecturer claims 'zero divides zero' is false because 0 is specifically excluded from the definition of divides.
What say you?