Riddles of integers and remainders
Bhaskara II investigated solutions to the equation (100x + 90)/63 = y, where x and y have to be positive integers (whole numbers). One possible solution is x = 1530 and y = 2430. In the ancient Indian tradition, examples were invariably used because there were no algebraic generalisations. But this example generalises into the following theorem:
If there are positive integers a and b that are coprime (meaning?), every integer that is greater than ab - a - b can be represented as ax + by, with both x and y being non-negative.
Or consider the problem investigated by Bhaskara:
"Tell me at once, O mathematician, that number which leaves unity as remainder when divided by any of the numbers from 2 to 6 but is exactly divisible by 7."
The answer is 301. Remainder problems were also examined by Aryabhata I, Brahmagupta, Sripati (1039) and Bhaskara II. When generalised, they led to the remainder theorem.