We only need 7 numbers for modulus (or clock) arithmetic mod 7
including working with fractions. Explore how to divide numbers and
write fractions in modulus arithemtic.

Suppose an operator types a US Bank check code into a machine and transposes two adjacent digits will the machine pick up every error of this type? Does the same apply to ISBN numbers; will a machine detect transposition errors in these numbers?

Obviously?

Age 14 to 18 Challenge Level:

Find the values of $n$ for which $1^n + 8^n - 3^n - 6^n$ is
divisible by 6.