Claims

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2002_06_01_shparlinski: Shparlinski's Theorem 3 of 2002: for every epsilon, every large prime p and every residue c, about 4 epsilon^(-3) distinct integers up to p^epsilon have inverses summing to c; the first answer, refereed, credited by the site.

2004_03_22_croot: Croot's Theorem 2 of 2004 with k = 1: for every epsilon in (0, 1] there is an N such that every residue modulo every prime is a sum of N inverses of integers up to p^epsilon, at most N at small primes; refereed in Integers.

2006_03_01_glibichuk: Glibichuk's Theorem 3 of 2006: for every epsilon and every large prime p, every residue is a sum of 8([1/epsilon + 1/2] + 1)^2 inverses of distinct integers up to p^epsilon; the site's improvement to epsilon^(-2), refereed.

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