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I think it is worth noting that Euler conjectured there was no solution to any square of order 4n+2, but in 1960 it was proved that only orders 2 and 6 have no
by LudwigNagasena 5y ago
I think it is worth noting that Euler conjectured there was no solution to any square of order 4n+2, but in 1960 it was proved that only orders 2 and 6 have no solutions.
- gibolt 5y agoI think it is worth noting that not everyone gets 100% right. You're point would be most accurate if Euler was a Quantum computation expert. I haven't read his biography, so can't know for sure.
- M2Ys4U 5y agoEuler was so successful and prolific that the list of discoveries named after him is huge. So big, in fact, that a great many things are named after the second person to discover them. He's one of - if not the - greatest mathematicians in history.
- yakubin 5y agoGiven that it was just a conjecture, why is it worth noting? Getting back to the main topic, it wasn't only conjectured, but also proven.
- contravariant 5y agoIt's noteworthy because it's an a conjecture by Euler and because it's an example of hasty generalization. Either Euler jumped to conclusions almost laughably quickly or something interesting happens once n >= 10.
- LudwigNagasena 5y agoBecause the conjecture for the order 6 is just a particular case of his wider conjecture that he posited, it gives a bigger picture.
- freemint 5y agoWhat does "square of order 4n+2" mean here?
- tromp 5y agoA 4n+2 by 4n+2 square.
- dotancohen 5y agoThe term "order 4n+2" means a number of the form n (a positive integer) times four, then add two. So 6 fits (6 is 1 times 4, plus 2) and 10 fits (10 is 2 times 4, plus two) but 12 does not (twelve can not be made by multiplying a positive whole number by four, then adding two to that number). Thus a 6x6 square is permissible, as is a 10x10 square. But not a 12x12 square.
- dav_Oz 5y agoA square of x by x for x ∈ {2, 6, 10, 14, 18, 22 ... } = {2, every uneven n multiplied with 2} 4n+2 = 2*(2n+1)