io6 Mr. Woodhouse on the bidependence of the 
there must be a number (s) in the progression (o, 1, 2, 3 ....) 
±sQ 
V — I 
= ~ ; consequently, there must be a value of x, a e n 
-tJ 
■ V— 1 / — ■ — - iiTr-y — 1 
#e 4 =ax± v — 1 , since (Art. XI.) e , or e 4 
= ±f — 1 . 
Hence, one quadratic divisor of of — a n will be of the form af -f c? 
= (x-\-aV — 1). ( jr — a V — 1) ; another, as it has been al- 
ready shewn, will be of the form x*—a.\ 
There are only n different divisors, for (n odd) the i)th 
±n — 1 
ey: 
and 72th divisors are comprised under the form x =ae * n 
the succeeding divisors would be comprised under the form 
1 
x=ae 
zn 
■ae 
X £ 
+n — i 
zn 
± ^ r i V=i ±v: 
as 2n , (since g 
If x n -\-a v —o, then m 
=1 ) the same as preceding form, 
to have m always positive. 
V — i' 
Let 
zV~i 
=s — i,then (Art. XI.) the values of % are =±= 27 t, 
( 2S + 1 )pv / — I 
1 ; consequently, 
x=.ae 
n 
?v: 
Let 27 ? = p, then generally s 
±(2S-J- I ) 
s any number of the progression o, 1, 2, &c. 
±p /— 
“ V —I 
, ae 
or x n -\- a n =. ( y x‘ —< a\s n ^ 1 + s n 
or the values of x are a s 71 
n & c. 
+a", . 
S? 
\/: 
4. g v ™ J }4-a 2 ) &c. 
When 72 is odd, there must be a number (25+ 1 ) in the progres- 
sion (i,3,5,7,&c.) = 72 ,* consequently, one value of x must 
