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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?

Some Cubes

The sum of the cubes of two numbers is 7163. What are these numbers?

Em'power'ed

Find the smallest numbers a, b, and c such that: a^2 = 2b^3 = 3c^5 What can you say about other solutions to this problem?

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 $6$.