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N000ughty Thoughts

How many noughts are at the end of these giant numbers?

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Mod 3

Prove that if a^2+b^2 is a multiple of 3 then both a and b are multiples of 3.

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Common Divisor

Find the largest integer which divides every member of the following sequence: 1^5-1, 2^5-2, 3^5-3, ... n^5-n.

Number Rules - OK

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Try some numbers first - are you convinced?

For part two-

Now try to write the product or quotient of two square numbers in a general form - can you rewrite this expression so that it is a (a number) squared?

For part three -

What are all the possibilities for the units digit when you square any whole number?