On monochromatic sums of squares and primes
نویسندگان
چکیده
منابع مشابه
Sums of Primes and Squares of Primes in Short Intervals
Let H2 denote the set of even integers n 6≡ 1 (mod 3). We prove that when H ≥ X, almost all integers n ∈ H2 ∩ (X,X + H] can be represented as the sum of a prime and the square of a prime. We also prove a similar result for sums of three squares of primes.
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Abstract. In this paper we continue our study, begun in [11], of the exceptional set of integers, not restricted by elementary congruence conditions, which cannot be represented as sums of three or four squares of primes. We correct a serious oversight in our first paper, but make further progress on the exponential sums estimates needed, together with an embellishment of the previous sieve tec...
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We study whether sufficiently large integers can be written in the form cp+ Tx, where p is either zero or a prime congruent to r mod d, and Tx = x(x + 1)/2 is a triangular number. We also investigate whether there are infinitely many positive integers not of the form (2ap−r)/m+Tx with p a prime and x an integer. Besides two theorems, the paper also contains several conjectures together with rel...
متن کاملOn Sums of Primes and Triangular Numbers
We study whether sufficiently large integers can be written in the form cp+ Tx, where p is either zero or a prime congruent to r mod d, and Tx = x(x + 1)/2 is a triangular number. We also investigate whether there are infinitely many positive integers not of the form (2p−r)/m+Tx with p a prime and x an integer. Besides two theorems, the paper also contains several conjectures together with rela...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2007
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2006.09.007