We define b f(n) to be the smallest integer (a natural number) d such that numbers f(n1, n2, ..., nm), where n 1+n2+ ... + nm ≤ n are not divisible by d. For the given functions f : ℕm → ℕ, we will obtain the asymptotic characterisation of the sequence of the least non canceled numbers (bf (n))nℕ. In the case f :ℕ2 (k, l)→k3+l3∈ℕ, this characterisation can be rewritten in the terms of the permutations polynomials of finite commutative quotient ring ℤ/mℤ. There are situations in which we cannot expect formula for bf(n) to be simple, but we can provide the upper and lower bounds of it.
