"Cubum autem in duos cubos, aut quadrato-quadratum in duos quadrato-quadratos, et generaliter nullam in infinitum ultra quadratum potestatem in duos eiusdem nominis fas est dividere cuius rei demonstrationem mirabilem sane detexi. Hanc marginis exiguitas non caperet" (Nagell 1951, p. 252). In translation, "It is impossible for a cube to be the sum of two cubes, a fourth power to be the sum of two fourth powers, or in general for any number that is a power greater than the second to be the sum of two like powers. I have discovered a truly marvelous demonstration of this proposition that this margin is too narrow to contain." I don't think he had a general proof. He proved validity for third and fourth degree. If he had the general proof this would be unnecessary. However, we have the proof today. Personally I think the problem is queer: "It is not like this - prove it!" There must be millions of statements that are not true.
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The purpose of this blog is not to insult Homer Simpson or any other of your idols.
1782^12 + 1841^12 is not equal to 1922^12 . To prove the statement, don't use your hand-held calculator! Use your head!
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Summan av ett jämnt och ett udda tal kan inte vara ett jämnt.
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Summan av ett jämnt och ett udda tal kan inte vara ett jämnt.
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