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'Weekly Challenge 8: Sixinit' printed from http://nrich.maths.org/
Choose any whole number $n$ and calculate $n^3 + 11n$.
Is the answer a multiple of 6 for all choices of $n$?
The challenge is to explain why or why not.
Did you know ... ?
Modular arithmetic is widely used to verify automatically whether a number has been correctly entered to a system. Each identification number (e.g. for passports, bank accounts, credit cards, ISBN book numbers and so on) obeys a rule which makes it easy to check (most of the time) whether or not the number has been copied correctly. For this reason such numbers are also called check