Octave, 24 bytes

@(m,n)diff(fix(0:m/n:m))

The code defines an anonymous function. The output is a numeric array (row vector). When there is no this array contains at least one zero, which is falsy in Octave.

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Explanation

0:m/n:m produces an array of n+1 values from 0 to m with step m/n. fix rounds each entry towards 0, and diff computes consecutive differences.

As an example, here are all intermediate results for m = 7, n = 3:

>> 0:m/n:m
ans =
         0    2.3333    4.6667    7.0000

>> fix(0:m/n:m)
ans =
     0     2     4     7

>> diff(fix(0:m/n:m))
ans =
     2     2     3