160 ROYAL SOCIETY OF CANADA 
6. Ifp = n, the right hand-side of (B) is 
Zan DER pe 
the right-hand side of (C) is 
ZT NON D: 
and the right-hand side of (E) is 
n ! 
If 6 is an imaginary nth root of unity, and 
IL, = (a, + 4,0 +a, ... + a, 0) (a, 0 +07... + 431 07 + Gy) 
(4,0) +a, +a,0+....+ a, 0") 
then (C) takes the form 
(a + 0a, +... 4 04} — 2 (a, + Oa, +... . Pas)? + 
PO 2 Gee vay C1 2 ae 
SSE Ad e s-- «bn (F) 
If, in addition, a, =a, =....= a, = 1; then (F) becomes 
a= a eee ee (et dO... t= OO) eri 
(ai? Sh Oy Glyn nt (@) 
But since 
SS ep Sh EVE) ER ue LR AT 2) _yn—ly" 
= (1) (1 6 a ea) 
We have from (G) 
forn=2s+1 
aye Ao eae UNE. cs 1)2s + l,ç1ÿ +223 
(DE 6 Be a ay? slo Saone) ae 
28 
+(-1°°2(2s+1) =(28s+1)! (G’) 
forn=2s8 
(ly 2 Gee pee eee ne HET +los pe gs-2)2s 
+ “25047? +c? 225-251 GC 
