पाटीगणित (श्रीधराचार्य - प्राचीन संस्कृत टीका एवं प्रो. कृपाशंकर शुक्ल सविस्तार व्याख्या)

46 DETERMINATIONS
then
RCᵣ - Pᵣ = 1 , (2)
for r = 1, 2, ..., n .
But (Cᵣ/D)x / y = Pᵣ + Aᵣ / y ,
where Aᵣ is the remainder when (Cᵣ/D)x is divided by y , so that,
when x = D(Ry - 1),
Pᵣ = Cᵣ x / Dy - Aᵣ / y
= Cᵣ (Ry - 1) / y - Aᵣ / y
= RCᵣ - (Cᵣ + Aᵣ) / y (3)
Therefore, we must have
y > Cᵣ , for all r ,
or y > C_λ ,
where C_λ is the greatest of all C's.
Hence a solution of (1) is
x = D(Ry - 1),
y = C_λ + k ,
k being an arbitrary integer.
Sub-rule for finding another rate of purchase, when the capitals
are integral and the articles which are left after selling at
the general rate as also the amounts of money acquired by
selling the articles at the general rate have a common factor :
61. The articles which are severally left after selling
(at the general rate) (i.e., the remnant articles) as also the
amounts of money which are severally acquired by selling the
articles (at the general rate), being abraded by their common
factor (lit. divisor), the resulting equal amounts of money
(i.e., the equal sale proceeds) give another rate of purchase.
This rule relates to the case when D = 1 , and may be expressed
analytically as follows :
If d be the common factor of
P₁, P₂, ..., Pₙ
and ( C₁x - P₁y ), ( C₂x - P₂y ), ..., ( Cₙx - Pₙy ),
Indological Truths