Fermat’s little theorem gives a condition that a prime must satisfy:<\/p>\n\n\n\n
Theorem. If P is a prime, then for any integer A, (AP<\/sup> – A) must be divisible by P.<\/p>\n\n\n\n Let’s check: Presentation Suggestions:<\/strong> The Math Behind the Fact:<\/strong> Fermat’s theorem is a special case of a result known as Euler’s theorem: that for any positive integer N, and any integer A relatively prime to N: (Aphi(N)<\/sup> – A) must be divisible by N, where phi(N) is Euler’s totient function<\/em> that returns the number of positive integers less than or equal to N that are relatively prime to N. So when N is prime, phi(N)=N.<\/p>\n\n\n\n Fermat’s “little” theorem should not be confused with Fermat’s Last Theorem.<\/p>\n\n\n\n How to Cite this Page:<\/strong>\u00a0 Fun Fact suggested by: <\/strong> Fermat’s little theorem gives a condition that a prime must satisfy: Theorem. If P is a prime, then for any...<\/p>\n","protected":false},"author":7,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"tags":[3,10,103,49],"class_list":["post-297","page","type-page","status-publish","hentry","tag-easy","tag-numtheory","tag-primality-test","tag-prime"],"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/297","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/users\/7"}],"replies":[{"embeddable":true,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/comments?post=297"}],"version-history":[{"count":4,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/297\/revisions"}],"predecessor-version":[{"id":1438,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/297\/revisions\/1438"}],"wp:attachment":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/media?parent=297"}],"wp:term":[{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/tags?post=297"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
29<\/sup> – 2 = 510, is not divisible by 9, so it cannot be prime.
35<\/sup> – 3 = 240, is divisible by 5, because 5 is prime.<\/p>\n\n\n\n
This may be a good time to explain the difference between a necessary and sufficient condition.<\/p>\n\n\n\n
This theorem can be used as a way to test if a number is not<\/em> prime, although it cannot tell you if a number is prime.<\/p>\n\n\n\n
Su, Francis E., et al. “Fermat’s Little Theorem.”\u00a0Math Fun Facts<\/em>. <http:\/\/www.math.hmc.edu\/funfacts>.<\/p>\n\n\n\n
Lesley Ward<\/p>\n","protected":false},"excerpt":{"rendered":"