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Age 16 to 18 Short Challenge Level:

Choose any whole number $n$, calculate $n^3 + 11n$, and divide by 6.

For what values of $n$ is your answer a whole number?
Can you explain why?
 
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 codes.