/lcqiic crit /z= 5-5 dclnde fiimto g— i fict/^~4i, idco- 

 qiie /~ i; fumto porro ^ =: 2 crir /^ :=: 4,4, ideoque / = 4; 

 fumto aurcm ^—3, ob //71=49 eO^e poterit /—7, vnde 

 omnes valores ipfius / erunt 1,4, 5,7. Pro altero exemplo, 

 quo n-^i^ valor ^-O tantum dat /= i ; valor g~i prae- 

 bet fhzn^i^ hincque vel /1=2, vel /=3, vei f~6i 

 porro valor ^ — 2 praebct f h — 45 , vnde colligitur f ~ S i 

 dcniquc valor g = 3 '^^t fh — so, vnde iterum fsquitur 

 fi^St ficquc omnes valores pro / funt i, 2, 3, 5, 6. Hinc 

 ergo colligimus, quotics pro formula x x -{- ^i y y prodcat 

 P numcrus primus , tum fcmper fore vel P, vel 2,1', vel 

 3P, vcl 5 P, vcl 6 P, cerrum numerum formae xx-[-^iyj; 

 Veluti fumto / — i, quia eft 82 — 31=79, ideoqi:c nun-erus 

 primus, ftatim parct, hunc ipfum numcrum 79 in forma x x 

 -t-4i/rj non contincri, ncquc etiam eiiis dupium 158: at eius 

 triplum 237 cft 14' -f- 41.1". Simili modo pro P etiam re- 

 pcritur numcrus primus 73, qui ncque ipfe, neque.eius du- 

 plum, neque triplum ip proppfita form.a. contiuet>ir, s^C \er91 

 cius quintuplum 365 cft — is* -f- 41. i.'. 



Problema. 



Si n fuerit numerus negatiuus^ puta n zn — m , inuenirt 

 formulam generaUm pro omnibus ntimeris primis^ (]ui exftftere pos^ 

 fuiit diuifores cuiuspiam numcri formac x x — m y y, vel eiiam 

 fvrmae m y y — xx. 



S o 1 u t i o. 



§. 29. Solurio huius problematis inftituatur vti prae- 

 cedentis fcribcndo fciiicer — ;;/ loco ;;, tum vero fi P dcno- 

 tct diuiforcm primum formulac propofitac, quoniam is ncccs- 

 fario cflc dcbct pofitiuus, etiam numcrum i ncgatiuum accipi 



1 2 conuenic 



