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

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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.


Stage: 4 Challenge Level: Challenge Level:1

Consider numbers of the form $u_n = 1! + 2! + 3! +...+n!$.

How many such numbers are perfect squares?