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?