The familiar Pythagorean 3-4-5 triple gives one solution to (x-1)^n
+ x^n = (x+1)^n so what about other solutions for x an integer and
n= 2, 3, 4 or 5?

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.

Climbing

Age 16 to 18 Challenge Level:

The graph of $y=\sin x$ lies above the line $y=2x/\pi$ joining the
origin to the point $(\pi/2, 1)$. The graph of $\sin x$ lies below
the line $y=x$. Why? What does this tell you about $\sin x$?