Non-congruent numbers with arbitrarily many prime factors congruent to 3 modulo 8 (Q676761)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Non-congruent numbers with arbitrarily many prime factors congruent to 3 modulo 8 |
scientific article; zbMATH DE number 993539
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Non-congruent numbers with arbitrarily many prime factors congruent to 3 modulo 8 |
scientific article; zbMATH DE number 993539 |
Statements
Non-congruent numbers with arbitrarily many prime factors congruent to 3 modulo 8 (English)
0 references
7 July 1997
0 references
The author proves that if \(p_1, \ldots, p_\ell\) are distinct primes satisfying \(p_i \equiv 3 \pmod 8\) and \((p_j/p_i) =-1\), \(j<i\), then the product \(p_1\ldots p_\ell\) is not a congruent number. A consequence of this result is the existence of an infinite sequence of distinct primes congruent to 3 modulo 8 such that any product of these primes is a non-congruent number.
0 references
elliptic curves
0 references
non-congruent numbers
0 references
product of primes
0 references
