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Fermat's Little Theorem -- from Wolfram MathWorld
Source: mathworld.wolfram.com
Article summary:
1. Fermat's Little Theorem states that if a prime number and a natural number are given, then the theorem holds true.
2. It is sometimes called Fermat's primality test and is a necessary but not sufficient test for primality.
3. Fermat's Little Theorem shows that if a number is prime, there does not exist a base with such that possesses a nonzero residue modulo .
Article analysis:
The article provides an accurate description of Fermat’s Little Theorem and its implications for testing primality. It also provides historical context for the theorem, noting when it was first proved by Euler in 1749 and when it was first referred to as “Fermat’s Little Theorem” in various textbooks. Furthermore, the article includes references to other related topics such as Wilson’s theorem, Chinese hypothesis, Euler’s totient theorem, Fermat pseudoprimes, Carmichael numbers, etc., which adds to its credibility.
However, there are some potential biases in the article that should be noted. For example, the article does not provide any counterarguments or alternative perspectives on Fermat’s Little Theorem or its implications for testing primality. Additionally, while the article does mention potential risks associated with using Fermat’s Little Theorem as a compositeness test (e.g., false positives due to Carmichael numbers), it does not provide any detailed information about these risks or how they can be avoided. Finally, while the article does include references to other related topics such as Wilson’s theorem and Euler’s totient theorem, it does not provide any detailed information about these topics or their implications for testing primality.
In conclusion, while this article provides an accurate description of Fermat’s Little Theorem and its implications for testing primality, there are some potential biases that should be noted before relying on this source as an authoritative reference on this topic.