Book:Abu Kamil/Kitāb al-ṭarā'if fi'l-ḥisāb/Historical Note
Historical Note on Kitāb al-ṭarā'if fi'l-ḥisāb of Abu Kamil
Possibly the first work that investigates the number of solutions to a general indeterminate equation.
It arose from Abu Kamil considering the question of purchasing $100$ birds at $100$ drachma, the birds being:
- ducks at $2$ drachma,
- hens at $1$ drachma,
- doves $2$ for a drachma,
- ring-doves $3$ for $1$ drachma
- and larks $4$ for $1$ drachma.
- I went into this problem fully and found that there were $2,696$ valid answers. I marvelled at this, only to discover -- when I spoke of it -- that I was reckoned a simpleton or an incompetent, and strangers looked upon me with suspicion. So I decided to write a book ...
The specific number varies among $2,676$, $2,678$ and $2,698$, depending on which authority you quote. Some of them may indeed have got the number wrong.
He continues the theme in his Kitāb al-ṭair (Book of Birds).