This seems familiar

Number Theory Level 4

There is some number x for which the following is known.

x 2 = x + 1 x^2=x+1
x 3 = 2 x + 1 x^3=2x+1

If x 8 = a x + b x^8=ax+b for some constant integers a a and b b , what is a + b a + b ?


The answer is 34.

Alex Li by Alex Li , 21, USA

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1 solution

Alex Li
Mar 13, 2017

First off, if you didn’t notice, x is the golden ratio. But presented this way, I think it’s a bit easier to find the pattern.

I typed out this solution in google docs using their golden ratio symbol, but unfortunately it does not transpose so I will post a screenshot of the solution here (the little thing with a line through it in the solution is x)

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