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A closed-form solution might be given by a tree. Valuations of quadratic polynomials. (English) Zbl 1430.11004

Summary: The \(p\)-adic valuation of an integer \(x\) is the largest power of the prime \(p\) that divides \(x\). It is denoted by \(\nu_p (x)\). This work describes properties of the valuation \(\nu_2 (n^2+a)\), with \(a \in\ \mathbb N\). A distinction of the behavior of these valuations for \(a \equiv 7\) mod 8 or not is presented.

MSC:

11A07 Congruences; primitive roots; residue systems
11S05 Polynomials
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References:

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