Criteria of divisibility by 9 and 11 . In what follows I shall be using representation of a number in various base systems. The most customary is the decimal system. But, say, the French still use remnants of the system in base 20. Conversion between different bases is a good exercise that helps test your understanding of relevant techniques.
Theorem Let b be an integer.
The proof is based on Modulo Arithmetic . Therefore 164 is divisible by 4. This implies that divided by 7 the remainder will be 1. Alexander Bogomolny 2410920 .