Math Is Fun Forum

pi_cubed

Member

From: A rhombicosidodecahedron

Registered: 2020-06-22

Posts: 115

1959 IMO Problem 1

I was trying to find a solution to problem 1 of the 1959 IMO that didn't use the Euclidean Algorithm and I was wondering if someone could check my answer.

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pi³

Bob

Administrator

Registered: 2010-06-20

Posts: 10,140

Re: 1959 IMO Problem 1

hi pi_cubed

I hadn't come across these problems so many thanks for that.  The algebra is ok so your argument seems to depend upon

                    <the re-arranged expression is irreducible> implies <the original is irreducible>

I think that is ok (maybe it's even a theorem) but it's not something I've encountered before, so I'm having a think about that.

LATER EDIT.

It's trivial to show that 2/3 = 4/6

But <2/3 is irreducible> does not imply <4/6 is irreducible>

So a re-arrangement alone is in-sufficient; something more is needed I think.

Bob

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob