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Code to Zero

Find all 3 digit numbers such that by adding the first digit, the square of the second and the cube of the third you get the original number, for example 1 + 3^2 + 5^3 = 135.

Always Two

Find all the triples of numbers a, b, c such that each one of them plus the product of the other two is always 2.


This is a beautiful result involving a parabola and parallels.

Powerful Factors

Age 16 to 18 Challenge Level:

Why do this problem?

For practice in factorising polynomials.

Key question

What is the highest power of 5 we can find using a calculator?

Can we factorise this expression to get factors involving smaller powers of 5, so that all the powers of 5 can be found using a calculator?

Howdo you know if a number is divisible by 3?