128 GANITASARASANGRAHA. related to the smaller group-value obtained as above so that a treeper-like chain of successive quotients may be obtained in this case also. Below the lowermost quotient in this chain the optionally chosen multiplier of the least remainder in the odd position of order in this last successive division is to be put down The principle underlying the process given in the rule is the same as that expluned in the rule regarding Vallaha kuttikara-but with this difference naniely, that the last two figures m the chain here are obtained in different way. Again, from the rationale given in the footnote to rule in 115, Ch. VI, it will be seen that the agru, b, associated with the remainder in the odd position of order, has the same algebraical sign as is given to it in the problem; while the sign of the ana, b, assomated with the remainder in the even position of order is opposite to its sign as given in the problem II nce, when the continue division is carried up to a remainder in the odd position of order, the valne of arrived at therefiom is in relation to such an aga as has is sign nnchanged, on the other hand, when the contmuel division is carried up to a remainder in the even position of order, the value of e arrived at therefrom is in relation to an ayna that has its sign changed. When the number of emainders obtained 18 odd, the number of quotients in the chain is even, and when the remainders are even, the quotients are odd in number. As the agra associated with the last remainder is in this rule always taken to be positive, the value of arived at is in relation to the positive ugra, if the last remainder happens to be in the odd position of order. And it is in relation to the negative agra, if the last remainder happens to be in the even position of onder In other words, if the number of quotients be even, the value is in relation to the positive agia, and if the number of quotients be odd it is in relation to the negative agru. The value of a in relation to the positive or the negative aga being thus found out, the other value is arrived at by snbtracting this value from the divisor in the problem. IIow this turns out will be clear from the following representation - Ax + b B know that =an integer. Here let ac, AB 18 also an integer. Hence B then Ac + b B AB B Ac + b B an integer We A(B-c)-b or B 15 an integer. It has to be noted here that the common factor, if any of the three given numerical quantities is to be removed before the operation of continued division is begun. The last diviso and the ast iemanden being required to be equal it will invariably happen that these come to be 1. The mat, required to be chosen in the rule relating to the Vallikä-kultikāra and required to be written below the chain of quotients, is in this rule always 1, the last divisor being 1. Therefore the last divisor here takes the place of the mate in the Valirka-kuttikäru It will be sen further that the last figure of the chain obtained according to this rule, 1.e., +aya, is the same as the last figure in the chain obtained in the Falteld-he tharu by dividing by the last divisor Le sum of the aura and the product of the mat as multiplied by the last remainder.
