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Exhaustion

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

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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.

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After Thought

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.


The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.
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