IS 



DE RESOLVT I ON E 



Etiamfi ergo (3 non fuerit numerus pir , tamen irf 

 -vtroque ordine femiffis valorum ipfius x fuerit numeri 

 integri. 



Exemplum a 



2 3 . Propofita formula V ( 3. x x -I- (3 ' x -4- y ) m y , 

 inuenire infinitos valores integros ipfius x , 40/Zw.f Zw^ 

 formula raiionalis euadit, fiquidem vnus cajus conjiet. 



Praebeat cafus cognitus x r= a et yzzb , tum vero ob 

 a rr 3 capiatur p — V ( 3 # # -f- 1 ) , eritque # — 1 et 

 p^zi. Hinc pro (ecundo eafu habebimus : 



cx quibus formentur binae feries recurrentes , fecundu&as 

 has fcalas relationis : 



vnde obtinentur : 



Valores ipfius % \ 



2.a±b-\-l$ 

 ta + t-b-p 



i6a± ifb-\-j$ 



91 a± 56^-hi<5(3 



Z6za±209b-\- z -~-fi 



Valores ipfius f 



3 *+»£+■££ 

 i2.g-\r- yb-hzfi 



45 *±. &**'*-;; 



i6&a±9ib-\-2%$ 

 62^a±s62b^ 2 -f^ 



135* * ±780 £-4-22 5 (3 [234.0*+ I35i^+35?cp 

 etc, etc. 



Praete- 



