XV.—Essay towards a General Solution of Numerical Equations of all Degrees having Integer Roots

H. F. Talbot
1875 Transactions of the Royal Society of Edinburgh  
The method of solution which I have the honour to lay before the Society is founded upon an old and well-known arithmetical process called "casting out the nines." It consists in substituting for any number the remainder which that number leaves when divided by nine. As this remainder contains only a single figure, whereas the original number may contain any number of figures, it is obvious that if the remainder can be employed instead of the number itself, a great saving of time and trouble must follow.
doi:10.1017/s0080456800025990 fatcat:dk5uzpoxdnaozc5wcmuvcrmydy