(174) 
p WN (p14!) (W (v)-1) N (ps) (WV (p91). Mp). 
(N (pr)-1 ie Paps (=) u(d) , (n= i? py po +. pr) 
d 
(pa being equal to a prime number of one or two members: 
Pa ply Afk) for the number g(x) of those members of a complete 
system of rests (with the exception of the naught) according to 
modulus ~ which are prime to this. 
This formula proves directly that this number is divisible at least 
by 4 if n is odd and by the 4 power of 2 for any x, when » has 
at least two mutually differing prime factors; moreover it shows 
that when m and n are prime to each other we have the relation 
p (mn) = p (m) p (x). 
Ps Tog ee es S 
Ln 1__N (n)—l 
4 
are the members of a fourth part of a system of rests according to the 
modulus « which will henceforth be supposed to be uneven and 
among these 
?1) Og: e« e » Coln) 
4 
prime to , then there exist for each complex integer m prime 
to » of the considered region the congruences: 
e (mn) MA 
r msi” wl, (mod.n) (2 mR pepe 
„5, (m,n) =0, 1, 2, 3) (2) 
+ (mn) Fe a 
5, ni" @'», (mod. n) (Ar rn @) 
17, (m,n) = 0,1, 2, 3), 
where the numbers 7, resp. 9,, are distinguished from the numbers 
r, resp. ¢'a, by the arrangement only. By multiplication of the 
congruences of the second system we obtain the relation 
