Demonstrates the minimal number of distinct polynomials needed to avoid certain sum forms over finite fields.
We study an analogue of a classical arithmetic problem over the ring of polynomials. We prove that \(m = 5\) is the minimal number such that the sums of any two distinct polynomials in a set of \(m\) polynomials over \(F_2[x]\) cannot all be of the form \(x^k(x+1)^{}\).
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Luis Angel Cruz Gallardo (2026) studied this question.
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