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Purr-fection

What is the smallest perfect square that ends with the four digits 9009?

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More Mods

What is the units digit for the number 123^(456) ?

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Old Nuts

In turn 4 people throw away three nuts from a pile and hide a quarter of the remainder finally leaving a multiple of 4 nuts. How many nuts were at the start?

Obviously?

Age 14 to 18 Challenge Level:

Why do this problem?

As a simple exercise using modulus arithmetic where learners can make and test their own conjectures. By trying small values of n learners may make their own conjectures about when the expression is divisible by 6 and when it is not.

Key question

How can we write the expression as an equivalent expression modulo 3?