From the year c. 850 the book Ganita-Sara-Sangraha
contains the following:
Three merchants saw in the road a purse. One said, "If I secure this purse, I shall become twice as rich as both of you together."
Then the second said, "I shall become three times as rich."
Then the third said, "I shall become five times as rich."
What is the value of the money in the purse, as also the money on hand?
There are an infinite number of solutions. Find the smallest whole number amounts the merchants could have.
An example of a problem given in the Ganita Sara Samgraha Ⓣ which leads to indeterminate linear equations is the following:
<blockquote style="font-family: "Times New Roman"; font-size: medium; text-align: justify;">Three merchants find a purse lying in the road. One merchant says "If I keep the purse, I shall have twice as much money as the two of you together". "Give me the purse and I shall have three times as much" said the second merchant. The third merchant said "I shall be much better off than either of you if I keep the purse, I shall have five times as much as the two of you together". How much money is in the purse? How much money does each merchant have?
</blockquote>If the first merchant has x, the second y, the third z and p is the amount in the purse then
p + x = 2(y + z), p + y = 3(x + z), p + z = 5(x + y).There is no unique solution but the smallest solution in positive integers is p = 15, x = 1, y = 3, z = 5. Any solution in positive integers is a multiple of this solution as Mahavira claims.