INDETERMINATE PROBLEMS. 209 



f>*m z +/> % ~4mf>+m* + i {m % +i){p z + i)—^mp 



■ p*m % —2m/> 1 —f> t +m x +2m—i> ° r """ p % ((m— i) 1 — 2)+(w+i) 1 — 2 



In the fame manner, by finding the values of x in terms of 

 v, &c we obtain y = ^y-^V+^-^^-i , or = 



m 1 ((fi—i) 1 ~2)+(p+iy— 2 % 

 /> , (( W _ 1 ; i _2)+(w+i) i _2 



PROBLEM XIL 



To find three numbers ', the producl of any two of which, increafed 

 by unit f Jhall be a fquare. 



By hypothefis, xy-\-i =z v 2 , xz-\-i =: j% and yz-\-l = w % . 

 i. Transposing the firft equation, xy zz v 2 — i, and re- 

 folving, xXy — (v-{-i)(v— i), whence y = mv — m, and ^+i 



= mx ; confequently, i> = m+y zz mx—i, and x = OT , . 



2. Again, tranfpofing the fecond equation, xz = J 1 — i, 

 and refolving, xxz zz (s+i)(s — i) ; whence, z zz ps — p, and 



j-f-i =r px ; confequently, j =: z+ ^ = /># — I , and reducing, 

 x — - z y . But # == — ~- : wherefore «z 2 z -j- 2m 2 p =: 



2mp*+py i and j/ == "»'«+"»>-*»»* . 



3. Moreover, by the third equation, j/z == W 1 — I ; 

 whence, yXz = {w-\-i)(w — i), and y = qw — q, and w+i 



zz qz 1 wherefore, w zz ZtL ~ qz—i, and y zz g 4 z — 2?. 



Vol. II, d J But 



