The nth 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.

Take a complicated fraction with the product of five quartics top
and bottom and reduce this to a whole number. This is a numerical
example involving some clever algebra.

Old Nuts

Age 16 to 18 Challenge Level:

This can be solved by just working systematically with the information, thinking about which numbers are divisible by 4 and 3, and testing the possibilities.

Modulus arithmetic also provides an efficient way to solve the problem.