Hua’s theorem on sums of five prime squares in arithmetic progressions

Author:

Bauer Claus1

Affiliation:

1. 1 Dolby Laboratories 100 Potrero Avenue San Francisco CA 94103 USA

Abstract

It is proved that for a given integer N and for all but ⪡ (log N ) B prime numbers kN5/96 − ε the following is true: For any positive integers bi , i ∈ {1, 2, 3, 4, 5}, ( bi , k ) = 1 that satisfy Nb12 + b22 + b32 + b42 + b52 (mod k ), N can be written as N = p12 + p22 + p32 + p42 + p52 , where the pi , i ∈ {1, 2, 3, 4, 5} are prime numbers that satisfy pibi (mod k ).

Publisher

Akademiai Kiado Zrt.

Subject

General Mathematics

Reference23 articles.

1. Bauer, C. , A note on sums of five almost equal prime squares, Archiv der Mathematik , Vol. 69, No. 1 (1997). MR 98c :11110

2. On the exceptional set for the sum of a prime and the k-th power of a prime;Bauer C.;Studia Scientiarum Mathematicarum,1999

3. Sums of five almost equal prime squares;Bauer C.;Acta Mathematica Sinica,2005

4. On the Goldbach Conjecture in arithmetic progressions;Bauer C.;Rocky Mountains Journal of Mathematics,2006

5. The exceptional set for the sum of a prime and a square;Brünner R.;Acta Math. Hung.,1989

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