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On Spieß’s conjecture on harmonic numbers

✍ Scribed by Jin, Hai-Tao; Sun, Lisa H.


Book ID
122443297
Publisher
Elsevier Science
Year
2013
Tongue
English
Weight
342 KB
Volume
161
Category
Article
ISSN
0166-218X

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Let p be a prime k | p -1, t = (p -1)/k and γ (k, p) be the minimal value of s such that every number is a sum of s kth powers (mod p). We prove Heilbronn's conjecture that γ (k, p) k 1/2 for t > 2. More generally we show that for any positive integer q, γ (k, p) C(q)k 1/q for φ(t) q. A comparable l