1969/07/01 by H. F. Trotter · 3 citations
Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #History and Theory of Mathematics
paper · pdf · doi:10.1090/s0002-9939-1969-0244196-6
openalex publication_date 1969/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/03/11
has a solution in integers. (This and other basic facts stated here without proof can be found in various texts on number theory such as [I ].) An obvious necessary condition for (1) to have a solution is that no factor of d be congruent to 3 modulo 4. The result that this condition is sufficient if d is prime goes back to Legendre; the general problem has been investigated by a number of authors. (See the introduction and list of references in [2].) The theorem we give below does not seem to have been noted explicitly. It is quite elementary and leads directly to various sufficient conditions for the solvability of (1). The theorem and its proof were suggested by the proof given in [1, p. 185] for the case that d is a prime.