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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?

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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.

Sixational

Age 14 to 18 Challenge Level:

The $n$th term of a sequence is given by the formula

$n^3 + 11n$.

Find the first four terms of the sequence given by this formula and the first term of the sequence which is bigger than one million.

Prove that all terms of the sequence are divisible by $6$.