#### Enestrom Number

598

#### Fuss Index

6

#### Original Language

Latin

#### Published as

Collection article

#### Published Date

1785

#### Written Date

1775

#### Content Summary

Euler begins by noting Lagrange’s work on the divisors of numbers of the form *Btt*+*Ctu*+*Duu* and his contribution to the 'knowledge' or 'science' of numbers. He includes the following problems: (1) find the divisors of *pp*+*nqq*; (2) transform *frr*+*grs*+*hss*, for which 4*fh*–*gg* = *4n*, into a diferent form *f'tt*+*g’tu*+*h’uu*, for which *g’ < f’* and *g < h’*, while still maintaining the property 4*f’h’–g’g’* = 4*n*; (3) find all the prime divisors of numbers in the form *pp*+*nqq*, where *p* and *q* are relatively prime with respect to *n*; and (4) find all the prime divisors of numbers in the form *pp*–*nqq*, where *p* and *q* are relatively prime with respect to *n*. Then a big theorem answers everything.

#### Original Source Citation

Opuscula analytica, Volume 2, pp. 275-314.

#### Opera Omnia Citation

Series 1, Volume 4, pp.163-196.

#### Record Created

2018-09-25