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math.NT2026
More sum-product type counterexamples: products with shifts and
Oliver Roche-Newton, Carl Schildkraut, Audie Warren
Adapting the construction disproving the sum-product conjecture over present in Bloom, Sawin, Schildkraut and Zhelezov, we show the existence of a constant and ar…
math.NT2026★ 1 cited
The sum-product conjecture is false for real numbers
Thomas F Bloom, Will Sawin, Carl Schildkraut +1
We disprove the sum-product conjecture for real numbers by constructing arbitrarily large (whose elements are algebraic integers in a number field of degree $…