{"id":319,"date":"2019-06-26T23:34:33","date_gmt":"2019-06-26T23:34:33","guid":{"rendered":"http:\/\/funfacts.104.42.120.246.xip.io\/?page_id=319"},"modified":"2020-01-03T23:52:57","modified_gmt":"2020-01-03T23:52:57","slug":"tamrefs-last-theorem","status":"publish","type":"page","link":"https:\/\/math.hmc.edu\/funfacts\/tamrefs-last-theorem\/","title":{"rendered":"tamreF’s Last Theorem"},"content":{"rendered":"\n

Here’s an amusing theorem that is very easy to prove, which we’ll call tamreF’s Last Theorem<\/em>. In fact it is tamreF’s only known theorem. It says:<\/p>\n\n\n\n

The following equation 
<\/em>Nx<\/sup> + Ny<\/sup> = Nz<\/sup> 
<\/em>has no solutions in positive integers for N greater than 2.<\/em><\/p>\n\n\n\n

This theorem has not been unsolved for centuries; in fact, it was solved as soon as it was posed. It is much easier to prove than its counterpart:\u00a0Fermat’s Last Theorem.<\/p>\n\n\n\n

The Math Behind the Fact:<\/strong>
The proof is ridiculously easy; consider the equation in base N. Perfect powers of N consist of a 1 followed by many zeroes. Adding two such numbers cannot be a number of that form unless N=2 and the 1’s are in the same position.<\/p>\n\n\n\n

How to Cite this Page:<\/strong> 
Su, Francis E., et al. “tamreF’s Last Theorem.” Math Fun Facts<\/em>. <http:\/\/www.math.hmc.edu\/funfacts>.<\/p>\n\n\n\n

References:<\/strong>
I have been told that the reference is in a Martin Gardner book, but I don’t have the reference!<\/p>\n\n\n\n

Fun Fact suggested by:<\/strong>
Arthur Benjamin <\/p>\n","protected":false},"excerpt":{"rendered":"

Here’s an amusing theorem that is very easy to prove, which we’ll call tamreF’s Last Theorem. In fact it is tamreF’s...<\/p>\n","protected":false},"author":7,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"tags":[3,176,10],"class_list":["post-319","page","type-page","status-publish","hentry","tag-easy","tag-fermats-last-theorem","tag-numtheory"],"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/319","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=319"}],"version-history":[{"count":3,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/319\/revisions"}],"predecessor-version":[{"id":1708,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/319\/revisions\/1708"}],"wp:attachment":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/media?parent=319"}],"wp:term":[{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/tags?post=319"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}