In number theory, the numbers of the form x² + xy + y² for integer x, y are called the Loeschian numbers. These numbers are named after August Lösch. They are the norms of the Eisenstein integers. They are a set of whole numbers, including zero, and having prime factorization in which all primes congruent to 2 mod 3 have even powers (there is no restriction of primes congruent to 0 or 1 mod 3).

Properties

• Every Square number is a Loeschian number (by setting x or y to 0).
  • Moreover, every number of the form ${\displaystyle (m^{2}+m+1)x^{2))$ for m and x integers is a Loeschian number (by setting y=mx).