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# Title: Leibniz-Handschriften zur Mathematik LH 35, 4, 3
# Folio 38r, page id 00068000:0075
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IM Numeris integris quaeritur bc + C = vV sit c=+ fiet bct vr 1 ∞tli0
oco f +1 bco p V 2b  p 2D bco
AV
sit b= 19 et C = 1. fiet 19c0 + 1 = vv Ergo
oportet ve esse quadratus, qui per 19 divisus relinquit 1. Tales sunt quadrati a numeris 19n + 1. posito
n esse numeros naturales ordine sumtos. seu v = i9n + 1 et fuot ig102 + 1 = (. 19. 19 nN + 2. 19n a 1
seu cot= ionn + 2p Ergo co divisibile per n a con etgr = defon n= effah
a4d
Jh et co: n = deffg, et fit 8effg = 19 effgh + 2 Ergo 2 dicidi potest
p et ( et 1
per effo. Ergo f - 1 et e, et G = 1 vel e =2 vel g = 2. si, f, e,9 sut l. fit d = 19h +2
Ergo videndum quinam qu biquadrati dvisi per i9 relinquant 2
typta
videndum et qui biquadratus divisus per quem biquadratum relinquat 2
redennd ad (9C0 +1 = vV, quia habemus limitationem ipsorum V, ut sit ion +c., patet
Dividi posse 1nco per 19n + 1, ita ut residuus sit 1, et residuum etiamfore l.
s 19co dividatur per vv, seu perqu (19n +1) 
ete v - 1 = ign
Ergo A quia ergo 190 potest dividi per v - 1 divididebet per ign, et per 1912 +2
et
Co
e vel 29+ vel dd, vel
con
vel 29h vl 2dh set l
d vel 2ch vel adh et fit Con = 19n + 2 = d = 19h + 2 vel
vet 168 =  19. 2h + 2 vel _ 2d = 19. 8d4+2 vel, 16d4 = 19. 16 +2
ad est d = 19h +2 vel 8d4 = 19tY + 1 vel Ad - 19. 4 +1 vel gd- 19. 8h= + 1
eugie
cer
a
h
1g, id est
D=1 divisib. per 19, oportt vel dd + 1, vel dd-
d-1 vel d+ 1, vel dd +1 erit divisibile per 19
esse divisibi