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Let $n$ be a positive integer.
STEP Mathematics I, 1996, Q3. Question reproduced by kind permission of Cambridge Assessment Group Archives. The question remains Copyright University of Cambridge Local Examinations Syndicate ("UCLES"), All rights reserved.
This problem asks you to use your curve sketching knowledge to find all the solutions to an equation.
Can you find a three digit number which is equal to the sum of the hundreds digit, the square of the tens digit and the cube of the units digit?
How many numbers are there less than $n$ which have no common factors with $n$?