ब्राह्मस्फुटसिद्धान्त (ब्रह्मगुप्त - शून्य, कुट्टक, बीजगणित एवं सम्पूर्ण २१ अध्याय सान्वय सटीक)

234 BRAHMAGUPTA AS AN ALGEBRAIST
Putting Q=2, we get x=40 and y=24, which is the least
solution.
Assuming now that the residues of the revolution (maṇḍa-
laja-śeṣa) of Saturn and Mars are 24 and 40 respectively, we have
to obtain the ahargaṇa (which means the number of mean civil
days elapsed since the beginning of Kaliyuga, or, in fact, any
epoch).
The revolution-number of Saturn is 146564, and the
number of civil days in a yuga is 1,577,917,500. In the present
problem, these are respectively the dividend and the divisor.
Their H.C.F. is 4, so that dividing them out by 4 we get 36641
and 394,479,375 as the abraded dividend and abraded divisor
respectively. We have, therefore, to solve the pulveriser
36641x–24
────────── = y
394479375
where x and y denote the ahargaṇa and the revolutions respecti-
vely made by Saturn.
Mutually dividing 36641 and 394479375, we get
36641) 394479375 (10766
394477006
─────────
2369) 36641 (15
35535
─────
1106) 2369 (2
157) 1106 (7
1099
7) 157 (22
154
3) 7 (2
6
──
1×27–24=3)3(1
3
──
0
We have chosen here the number 27 as the optional
number (mati). In fact, mati may be chosen at any stage after
an even number of quotients are obtained.