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We use Green's transference principle to show that any subset of the $d$th powers of primes with positive relative density contains nontrivial solutions to a translation-invariant linear equation in $d^2+1$ or more variables, with explicit quantitative bounds.
Original languageEnglish
Pages (from-to)2341–2374
JournalInternational Mathematics Research Notices
Issue number8
Publication statusPublished - 11 Jan 2017

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