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Version. The 20-page slide PDF has the same title and authors as the related article manuscript but carries no date or venue on its own pages. Michael Filaseta's official seminar list identifies a talk with this exact title and joint authorship as an invited lecture at the AMS Sectional Meeting in Urbana-Champaign on 20 March 1999, with slides. The slides are therefore identified by that event rather than dated from a file name.

The slides are distinct from the 10-page article manuscript; both versions are identified on the source card. That manuscript corresponds to the work published in Illinois Journal of Mathematics 44 (2000), 633--643. Its pages are internally numbered 1--10 and carry no journal-facsimile header, so publisher-facsimile or exact published-version identity for the manuscript has not been established.

Statement comparison

Slide 11, headed "Theorem (F., Ford, Konyagin)", gives the lecture version of the Corollary on manuscript p. 3. In both versions, $f,g\in\mathbb Z[x]$ have nonzero constant terms and $\gcd(f,g)=1$; $r_1,r_2$ count their nonzero terms; and

$$N=2\lVert f\rVert^2+2\lVert g\rVert^2+2r_1+2r_2-7.$$

Both impose

$$n\geq\max\left\{ 2\cdot5^{2N-1}, 2\max\{\deg f,\deg g\}\left(5^{N-1}+\frac14\right) \right\}.$$

They also give the same two exceptional cases:

1. $-f(x)g(x)$ is a $p$th power for some prime $p\mid n$;
2. for one sign $\epsilon\in\{1,-1\}$, one of $\epsilon f(x)$ and $\epsilon g(x)$ is a fourth power, the other is four times a fourth power, and $4\mid n$.

The slide writes the second case with "$\pm f(x)$ or $\pm g(x)$"; the manuscript makes explicit that one sign $\epsilon$ serves both polynomials.

The slide says that outside these cases the non-reciprocal part of $f(x)x^n+g(x)$ is irreducible. The manuscript Corollary states the conclusion more precisely: that part is irreducible or identically $1$ or $-1$. Thus the slide is an abbreviated presentation of the manuscript result, not a stronger version. In particular, the minus sign in $-f(x)g(x)$ occurs in both versions.

Slide 3 also states the distinct odd-modulus covering question recorded as Problem 7. Slide 12 gives the Capelli reduction that motivates the bivariate irreducibility target; it does not add a separate proof to the manuscript.

Read scope. Slides 1, 3--6 and 11--12 were read against their rendered pages. The comparison source was the 10-page article manuscript, especially manuscript pp. 1--3. Official publication records establish the publication identity of the corresponding work, not the byte identity of the manuscript read; no publisher facsimile was acquired or identified. No proof in either version was independently checked or reconstructed.

Bears on. Problem 7.