SOLVTIO QVORVNDAM 



PROBLEMATVM 



DIOPHANTAEORVM. 



A u c t o r c 

 L. E V L E K O. 



Problema i. 



Inuenire d.vo qnalratorum paria XX, yy ct //, WW, 

 it.i \t tiim (.V .V -\- y y^ (/ 1 x x -f- u ujy) quatn 

 [x X -Vy j) 0' « -^' X ■{- t tyy) fiat numtrus qiradraius. 



A n a I y /i s. 



1. Primo patct , cjuiciinque bini numcri tam 

 pro .r, y quam jro ;, u fucrint inuenti ., corum ac- 

 que mulupla vclnti ax, ay ct S;, § ?< quaefito 

 acquc (atisfaccre ; ficque probkma ita rcllringi con- 

 vcnict , vt tam x ct 7 quam / ct u fint numeri 

 primi intcr (c. 



2. Incipiamns a formula priori (xx-\-yy)[tt xx 

 + ?/Kj'j), qu:ie pofita huic quadrato {x x +yyy x x yj 

 (p p ■+• g '/)' aequalis fit 



ttxx-hu uyy zz. x xyy [x x \yy) (( pp - (? ^)* -K 2 P </)') 

 \nde coiicluditur 



tx-xyix ipp-qq) + 2iqy)i uy=:xy{y{pp-qq)-tfqx) 

 ficquc crit 



tZZXyipp-gq^-^-ipqyyi U—Xy{pp-qq)-ipqxX, 



