562 
n=20p, 20p+1,... 20p419 
1200 
== (—5, —8, —5, —7, —5, 3,0, 3 Ms ty 
a £8000 ° 
? 
OAN SKO NON RO OD — 7). 
From the preceding formulae we may deduce the several results 
Wor pO (Gre > HE) 
To illustrate this, taking n =10p + 7, we obtain 
(n* + 76n? + 1901n* + 17366n + 419302, 
1 48000 
W, =i lors Wp LAB) 
1 
Wenn 600) 
W, 00 24n? + 840n + 6300 ) 
taal AE) 
We = gon aor 1207) 800K) 
] 
* 48000 { en 
>= 3600 ) 
and finally 
= W. 
We 48000 
=p + 1)(p + 2) p® + 22p + 9). 
That this value is an integer may he easily seen by writing 
= W..=3P(p + 1)(p -+ 2) (10 p + 22) + 3(p + 1) (p + 2). 
Comparing the general formula of SYLVESTER 
——— (nf + 76n* + 1910n? + 17516n + 43329) 
o” ent t 
(lg e-% 4) (l—e eat) . (l-e7e 7) (0) 
with the formula (7), it is evident that in his formula @” ought 
to be replaced by or. This makes no difference in the values W, 
and W,. In the example treated by Syuvesrer 
ot 2,3, 4, Hoe, t 6x, =n 
the values of W,, W,, W, and W, however want correction. 
VP) 
a 
