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Shades of Fermat's Last Theorem

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 the positive integer solutions of the equation (1+1/a)(1+1/b)(1+1/c) = 2

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.


Age 16 to 18 Challenge Level:

For the first part draw the graph of $\sin x$, draw the line segment joining the origin to the point $(\pi/2, 1)$ and draw the line $y=x$.

For the second part draw the graph of $\tan x$ and draw straight line segments joining the origin to the points $(a, \tan a)$ and $(b, \tan b)$.