About Fermat's last Theorem?beal etc

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I could not get the point why people are so crazy about FLT?, I have seen that there is no much difference in Beal conjecture as well as FLT. Why people will pose such conjecture and announce prize money, when there is no application/use in Math/science. If there is any use of applicability of this theorem in reality, where we can apply? what are the uses in real life? If you know, please let me know. Clearly, I want to lean the applicability of the FLT or beal in real life? If there, let me know as well as other members.

Thanks in advance -Richard Sieman

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Why people will pose such conjecture and announce prize money, when there is no application or use in Math/science.

To answer a question with a question: Why do people offer up to millions of dollars for guessing six numbers out of $49$, or winning a poker tournament, when that has even less applicability in math, life, and science ? :-)