Converse
The converse of Fermat's little theorem is not generally true, as it fails for Carmichael numbers. However, a slightly stronger form of the theorem is true, and is known as Lehmer's theorem. The theorem is as follows:
If there exists an a such that
and for all prime q dividing p − 1
then p is prime.
This theorem forms the basis for the Lucas–Lehmer test, an important primality test.
Read more about this topic: Fermat's Little Theorem
Famous quotes containing the word converse:
““You are old, Father William,” the young man cried,
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You are cheerful, and love to converse upon death:
Now tell me the reason, I pray.”
“I am cheerful, young man,” Father William replied;
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In the days of my youth I remembered my God,
And He hath not forgotten my age.””
—Robert Southey (1774–1843)
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About the new school of the pseudo-phallic ...”
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“It is said that desire is a product of the will, but the converse is in fact true: will is a product of desire.”
—Denis Diderot (1713–1784)