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# Title: Leibniz-Handschriften zur Mathematik LH 35, 15, 5
# Folio 9r, page id 00068207:0013
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sroblema Ecibnitranum
Esto AEquatio: bx + 1 = yq quaeritur ejus solutio in integris,
posito b estenunerum datum, x et y qua sitos, et yminorem quamb.
sctitur autem solutio ea lege, ut distimulentur faciores datinumen b.
solatio. Cum yponatur minor quam b, ponatur 9 + Z = b
et sic b - 2 - 9.
b-267 +7 = yy = bx +1
hoc est b= 2b4 + -,
X. Jam si Z supponatur unitas este.
tunc evanescit quantitas + 2 - 1
remanebitue b2=2b
= b - 2 = X. et supra b - 2 - b - 1 = y.
Est igitur Solutio universalis pro quovis num. dato b. si 2 ponatur = 1.
oportebit autem b datum semper esse majorem quam 2. ut ita 2 possit
abstrahi ab, quandoquidem b - 2 = X. et b -, - y.
Troba: C
to b = 6. 7 = 1. erit b - 2 = 4 = X. b = 1 = 5 - y
atque ita bX +1 = 25 = v7
Qnodsi vero proratione dati num. b, possit z esce major gnitate, is debet
assumitalis, ut 3 exacte dividi pescit per b sed hnce numerum Z invempe
aequo difficile ac problema solvere. Sit quotiens divisionis V quaeritur ergo ZZ- 1 = b
Ve
Sn exemplo detur b =8. Hlic si Z assumatur = 1. habetur per priorem
Canonem y = b - 1 = 7. et X = b = 2 = b.
dentemus autem, an 7 possit assumi talis, cujus Dtum 2 dividi possit pec b
seu per 8. et inveniuntur duo, 9 et 25. Nam
e-
C=3. f= 1 = 8 dividitur per b = 8 e per 12
et 7 = 5. 7=1 = 24 dividitur per b = 8 et per 3
Aaque adrem: b = 8. 7 = 3. Ergo b = Y - 5 - y. QuadX vero erit
0
ex. (an: b= -267. + Z=1 - 69 48 + 9 -1 = 24
C
Rarsus b - 8. 2 = 5
D
3 - y
e
Guoad X, erit b2 2b2 + 2=1 = 64 - 80 +25 - 1 -
3=
6