Saidak, Filip On Goldbach’s conjecture for integer polynomials. (English) Zbl 1192.11074 Am. Math. Mon. 113, No. 6, 541-545 (2006). Introduction: We give a short proof of the fact that every monic polynomial \(f(x)\) in \(\mathbb Z[x]\) can be written in the form \(f(x)=g(x)+h(x)\), where \(g(x)\) and \( h(x)\) are both irreducible monic polynomials in \(\mathbb Z[x]\). For the number \(\mathfrak R(f;y)\) of representations of \(f(x)\) as a sum of two irreducible monics \(g(x)\) and \(h(x)\) in which all coefficients of \(g(x)\) and \(h(x)\) are bounded in absolute value by \(y\), we prove that \[ y^ d\ll_ f\mathfrak R(f;y)\ll_ fy^ d \] as \(y\to\infty\), where the notation ‘\(\ll_ f\)’ means that the constant could depend on (the degree and coefficients of) the polynomial \(f(x)\). Cited in 1 ReviewCited in 2 Documents MSC: 11P99 Additive number theory; partitions 13B25 Polynomials over commutative rings PDFBibTeX XMLCite \textit{F. Saidak}, Am. Math. Mon. 113, No. 6, 541--545 (2006; Zbl 1192.11074) Full Text: DOI Link