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.

Which is larger cos(sin x) or sin(cos x) ? Does this depend on x ?

Shades of Fermat's Last Theorem

Age 16 to 18 Challenge Level:

There are exactly three solutions of the equation $$(x - 1)^n +
x^n = (x + 1)^n$$ where $x$ is an integer and $n= 2, 3, 4$ or $5$.
Prove this statement and find the solutions.