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e.g. n = (n1 + n2+ .. + nm)
where n is number and m no of slices.
n will be positive integer and m won't exceed 50.
Edit: slices should be of distinct values.
Another can be,
a) All Integers n1 = n2 = n3 =.....= n[m-1] = int(n / m) and nm = n - (n1 + n2 + n3 +.....+ n[m-1])
b) Floats n1 = n2 = n3 =.....= n[m] = n / m
I feel the problem can be more serious if you want the parts to be in certain fashion or distribution.
n1 = n2 = ... = n(m-1) = 0
nm = n
Here's another solution:
n1 = n2 = ... = nm = n/m
Others have asked relevant questions. Assuming you want the numbers to be integers, and as equal as possible, then compute:
k_min = floor(n/m)
excess = n-k_min*m
n1 = k_min + 1
...
n(excess) = k_min + 1
n(excess+1) = k_min
...
nm = k_min
You could also put all the excess in one place, so you have
n1 = n2 = ... = n(m-1) = k_min
nm = k_min + excess
This is still fairly trivial.
I sense there are yet more requirements you're not telling us.
I think your problem description is missing something; otherwise n1 = n2 = n3 ... = n[m-1] = 1, nm = n - m + 1 is a trivial solution.
In that case, [1, 2, 3, ... m - 1, n - m*(m-1)/2] is a trivial solution.