The problem is to find 7 positive integers a, b, c, d, e, f, g such that • a²+b²=d², • a²+c²=e², • b²+c²=f², • a²+b²+c²=g². According to Wikipedia (https://en.wikipedia.org/wiki/Euler_brick …) it was shown that the length of the shortest edge must be greater than 5×10¹¹. So good luck everyone!
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Is it known that a solution exists, but we just haven't found it yet, or is it an open problem whether or not it exists? Seems to be the latter, based on Wikipedia.
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I have a nice proof of this, but a tweet is too small to hold it.
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Like, 3²+4²+(3*4)² ?
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@rationalexpec, olha que interessante. Os pontos dessa imagem são os vertices e diagonais do cubo. Elas todas aparentemente formam funções tangente. Se a função fosse descoberta, ela poderia dizer se existe um cubo nessa configuração?pic.twitter.com/9YNGozR9kj
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This Tweet is unavailable.
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2525 ? 693^2+140^2+480^2+2376^2=2525^2
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Is there any reward for solving it?
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a=3 b=4 c=5i d=5 e=4i f=3i g=0 is the smallest non-trivial solution. You can replicate this for all pythagorean triplets. Only point to note: 3 of the values have to be imaginary.
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This was no wonder the last reply on this post. Must have set people thinking of a solution. I finally got it. It is now posted on my blog.
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