text: what is fermats theory, and harmdats theory? can anyone give me the rudiments please i assume that you are referring to fermats last theorem - it is very simple : this equation   x to the power of n + y to the power of n equals z the power of n  has no solution for non-zero integers x, y, and z if n is an integer greater than 2.    what is so controversial about this is fermat proposed this equation and claimed to have come up with a way to prove that this is correct in the margin of his notes. however, he didn't write down his proof. it was, however finally proved (the 90's i think).   never heard of harmdats theory though and a quick search on google turns up nothing - are you sure you have the name right?  edit : it just occurred to me that you could be refering to fermats little theorem. this is less known but used far more regularly. it is used to test if large numbers are not prime. basically, it states that,   x to the power of (p-1) = 1 mod p  where p is a prime which is not a factor of x and p is greater than a which is greater than or equal to 1. if this is false for any value of x then p is not prime.  although this is true for all primes however it is also true for some non-primes. therefore this can only be used to prove that a number is definitely not a prime, not that it is definitely a prime.