
Easiest IMO problems that will make you feel like a Genius - gencode
https://iq.opengenus.org/easiest-imo-problems/
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brmgb
The problems are good but the article is not that great.

Some of these "proofs" are quite sloppy and the complete ones often entirely
fail to highlight where their key ideas come from.

For example, let's look at their proof for the IMO 1964 Problem 1. Their
introduction is plainly stating : when 2^N is divided by 7, there can be only
3 different remainders. Well, properly proving that is 90% of the whole
problem. You can't just skip over it and call what you wrote a proof.

Note that doing it is far from hard. You have to split 2^n into 2^3n, 2^(3n+1)
and 2^(3n+2) and do a simple proof by recursion of the stability of their
congruence modulo 7.

The problem is indeed relatively easy because you can find the trick of
splitting 2^n this way by systematically looking at 2^n mod 7 for small n.

On the other hand, their proof of the IMO 1984 Problem 1 is complete but they
entirely fail to convey from where the factorisation at the heart of it comes.

