INDETERMINATE PROBLEMS. 209 



— /)*ct'+/>'— 4ct /. +>b'+i (m'+iXft' + O— 4"'/' . 



~ p*m^—2mp^—f>^+m'+2m—i' °*' "~ />»((m— l)*— 3)+(ct+i)*— 2 



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

 V, &c. we obtain y = '-y-^'"'fi+P\-'"l+'P-- , or = 



/,»((m_l)»_2)+(«+i)'— 2 



PROBLEM Xir. 



To find three numbers^ the produB of any two of which, increafed 

 hy unit, pall he a fquare. 



By hypothefis, xy+i = v\ xz-\-i = j% and yz-^l = w\ 



I. Transposikg the firft equation, xy = v'' — i, and re- 



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



2m+y 



= mx ; confequently, v =. -^±L = mx—i, and x = 



■'■J 



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

 and refolving, xXz = (j+i)(-f — i) 5 whence, z ■=. ps—p, and 



j+i =z /'x; confequently, J =: -^^ = /'-ic — i , and reducing^ 

 * = i±±. But X =: —P- : wherefore m'z + 2m'p — 



p^ m 



zmp^-^p^y, and y = '"'^+''"'fi-^'"P' , 



3. Moreover, by the third equation, yz =. to'— i ; 

 whence, yXz =. (to+i)(w — 1), and y =. qw — q, and to+i 



= qz ; wherefore, w = Ztf_ = ^z — i, and / = q^z — 2?. 



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