You may also like
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?
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
Show that if $n$ is a positive integer then
$$n^{1/n} < 1 + \sqrt {{2\over {n-1}}}.$$
Show that $n^{1/n}\rightarrow 1$ as $n\rightarrow \infty$.
Find the maximum value of $n^{1/n}$ and prove that it is indeed the maximum.
Copyright © 1997 - 2023. University of Cambridge.
All rights reserved.
NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.