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A simple example that is hard to determine if it halts is to iterate through a,b,c,n and see if a^n+b^n=c^n. I.e. solve Fermat's last theorem by brute force. (I
by kens 14y ago
A simple example that is hard to determine if it halts is to iterate through a,b,c,n and see if a^n+b^n=c^n. I.e. solve Fermat's last theorem by brute force. (I won't spell out the iteration details.) If your software could determine if this halts or not, it would prove Fermat's last theorem. (Obviously since FLT has been proven, this particular case is known not to halt.)
- Luyt 14y agoInteresting read: "The proof itself is over 100 pages long and consumed seven yearsof Wiles's research time. For solving Fermat's Last Theorem, he was knighted, and received other honors." http://en.wikipedia.org/wiki/Wiles%27s_proof_of_Fermat%27s_Last_Theorem http://en.wikipedia.org/wiki/Wiles%27s_proof_of_Fermat%27s_L...
- nijk 14y agoThere is a paper online that proves fermat's last theorem in this way, by exploiting the C compiler's ability to optimize away non-terminating code that has no observable state changes.