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
k
≦
N5/96 −
ε
the following is true: For any positive integers
bi
,
i
∈ {1, 2, 3, 4, 5}, (
bi
,
k
) = 1 that satisfy
N
≡
b12
+
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
pi
≡
bi
(mod
k
).
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
Cited by
1 articles.
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