若a不能被素数p整除时,则 a~(p-1)=1 (mod p) (1) 这是著名的费马定理,其应用很广。但是它的逆命题不成立。 我国古代(大约2600年前)曾出现一个错误的命题:若n|2~n-2,则n是一个素数。 这个错误的观点,持续了很长一段时期,直到1819年才有人找出一个反例,即341|2~341-2,但341=11·31不是素数。从此,更多的反例被找出,例如561,645等等。人们把这 If a cannot be divisible by the prime p, then a~(p-1)=1(mod p) (1) This is the well-known Fermat’s theorem, which is widely used. But its contradictory proposition does not hold. In ancient China (about 2600 years ago) there was a wrong proposition: if n|2~n-2, then n is a prime number. This erroneous view lasted for a long period of time. It was not until 1819 that someone found a counterexample, 341|2~341-2, but 341=11·31 was not a prime number. Since then, more counterexamples have been found, such as 561,645 and so on. People take this