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 4fh–gg = 4n, into a diferent form f'tt+g’tu+h’uu, for which g’ < f’ and g < h’, while still maintaining the property 4f’h’–g’g’ = 4n; (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.