l -St*r3
98
THEORIA RESIDUORUM BIQUADRATICORUM.
Kc
A, quoties 6
B, quoties 6 = «
C, quoties a — 0
D, quoties 6 = 4«
Manifestum est, has regulas complecti casus omnes, quum pro 6 = 2«, vel
b eee 3« (mod. 5), . fieret ««-f-66 = 0, Q.E. A., quum per hypothesin p sit nu
merus primus a 5 diversus.
y
27.
Perinde inductio ad numeros —7, —11, —f-1 3, —j—17,
cata satisque producta sequentes regulas indigitat:
Pro numero —7.
« = 0, vel 6 = 0 (mod. 7)
b = 4 a, vel b = 5 a
b = a, vel b = 6 a
h = 2 a, vel 6 = 3 a
Pro numero —11.
b = 0, 5 a, vel 6 a (mod. 11)
b = a, 2>a vel 4 a
a= 0, vel b = 2a vel 9 a
b = 1 a, 8 a vel 10«
Pro numero
b = 0, 4a, 9« (mod. 13)
6 = 6«, 11«, 12«
« = 0 ; 6=3«, 10«
6 = «, 2«, 7 «
Pro numero —j— 17.
« = 0; 6 = 0, «, 16« (mod. 17)
6 = 2«, 6«, 8«, 14«
6 = 5«, 7«, 10«, 12«
6 = 3«, 9«, 11«, 15«
19, — 23 appli-