Fermat's Little Theorem - Converse

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:

    Who can converse with a dumb show?
    William Shakespeare (1564–1616)

    The Anglo-American can indeed cut down, and grub up all this waving forest, and make a stump speech, and vote for Buchanan on its ruins, but he cannot converse with the spirit of the tree he fells, he cannot read the poetry and mythology which retire as he advances. He ignorantly erases mythological tablets in order to print his handbills and town-meeting warrants on them.
    Henry David Thoreau (1817–1862)

    “You are old, Father William,” the young man cried,
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    Robert Southey (1774–1843)