Number Theory Textbooks to Finding the Best!

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Where I can I find good textbooks on Number Theory?:smile:
 
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This is going to sound sarcastic (but I'm really being sincere) but try a university library.

Even some small, two-year colleges, have libraries that have good textbooks on mathematics (and number theory).

If you want specifics, I'll get back to you on that one.

For a general approach, try Miller and Hornsby's Mathematical Ideas. It's designed primarily for education majors but I think it's a great book for the basics of a lot of math fundamentals (including number theory).
 
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Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
I'm interested to know whether the equation $$1 = 2 - \frac{1}{2 - \frac{1}{2 - \cdots}}$$ is true or not. It can be shown easily that if the continued fraction converges, it cannot converge to anything else than 1. It seems that if the continued fraction converges, the convergence is very slow. The apparent slowness of the convergence makes it difficult to estimate the presence of true convergence numerically. At the moment I don't know whether this converges or not.

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