Originally posted by Denny
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Actually, I indulged in a bit of light reading - I was reading about Fermat's Last Theorem. Fascinating stuff. Not that I'd expect a birdbrain like you to know anything about it. 
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In 1847 Lamé announced that he had a solution of Fermat's Last Theorem and sketched out a proof. Liouville suggested that the proof depended on a unique decomposition into primes which was unlikely to be true. However, Cauchy supported Lamé. The argument which followed indicates the totally different atmosphere surrounding mathematical research of this period from that which we know today. Perhaps we could illustrate the point causing this argument. Complex numbers of the form a + b√-3, where a, b are integers, form a ring. A prime number in this ring is defined in an analogous way to a prime integer, namely a number whose only divisors of the form a + b√-3 other than itself are those numbers with multiplicative inverses. In this ring 4 can be written as a product of prime numbers in two different ways
4 = 22 and 4 = (1 + √-3)(1 -√-3).
Gauss had proved around 1801 that numbers of the form a + b√-1, where a, b are integers, could be written uniquely as a product of prime numbers of the form a + b√-1 in an analogous manner to the unique decomposition of an integer as a product of prime integers. In fact, numbers of the form a + b +c2 where a, b, c are integers and is a complex cube root of 1, also have unique factorisation, and this can be used to prove the n = 3 case of Fermat's last Theorem.
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In 1847 Lamé announced that he had a solution of Fermat's Last Theorem and sketched out a proof. Liouville suggested that the proof depended on a unique decomposition into primes which was unlikely to be true. However, Cauchy supported Lamé. The argument which followed indicates the totally different atmosphere surrounding mathematical research of this period from that which we know today. Perhaps we could illustrate the point causing this argument. Complex numbers of the form a + b√-3, where a, b are integers, form a ring. A prime number in this ring is defined in an analogous way to a prime integer, namely a number whose only divisors of the form a + b√-3 other than itself are those numbers with multiplicative inverses. In this ring 4 can be written as a product of prime numbers in two different ways
4 = 22 and 4 = (1 + √-3)(1 -√-3).
Gauss had proved around 1801 that numbers of the form a + b√-1, where a, b are integers, could be written uniquely as a product of prime numbers of the form a + b√-1 in an analogous manner to the unique decomposition of an integer as a product of prime integers. In fact, numbers of the form a + b +c2 where a, b, c are integers and is a complex cube root of 1, also have unique factorisation, and this can be used to prove the n = 3 case of Fermat's last Theorem.
Then I suggest that you get out more as there is something called "life" going on around you and you appear to be missing it...
All maths and no play makes Denny a dull boy\girl. (delete as appropriate).
I take it back. Uncalled for upon reflection.
Have no fear, you are quite safe.
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