mersenneforum.org (https://www.mersenneforum.org/index.php)
-   Number Theory Discussion Group (https://www.mersenneforum.org/forumdisplay.php?f=132)
-   -   Devaraj numbers which act like Carmichael numbers (https://www.mersenneforum.org/showthread.php?t=23538)

Devaraj numbers which act like Carmichael numbers

In the ring of Gaussian integers 33 - 4*I = (2 - I)*(3+2*I)*(4-I) is a Devaraj number ( ref: A 104016 and A 104017 in OEIS ) which acts like a Carmichael number with reference to modified Fermat's theorem excepting when p = 5, 13 and 17 (norms of the three factors).
Recall modified Fermat's theorem: a^(p^2-1)==1 (mod p) where a is a quadratic algebraic integer.
{"ft_lang_label":"__label__en","ft_lang_prob":0.8194583,"math_prob":0.89529526,"size":995,"snap":"2022-05-2022-21","text_gpt3_token_len":309,"char_repetition_ratio":0.09889001,"word_repetition_ratio":0.72727275,"special_character_ratio":0.33869347,"punctuation_ratio":0.095,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99103767,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-01-25T11:01:33Z\",\"WARC-Record-ID\":\"<urn:uuid:647764bf-9362-416c-a366-926f035381f6>\",\"Content-Length\":\"4597\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:c6190d4a-6dc2-488c-b969-a26f367cfbd4>\",\"WARC-Concurrent-To\":\"<urn:uuid:0d912034-d214-498a-b842-5ca078fd2b2d>\",\"WARC-IP-Address\":\"216.92.123.112\",\"WARC-Target-URI\":\"https://mersenneforum.org/printthread.php?s=2a9bc6f58c2bb581c1f92d2dcc5d92cd&t=23538\",\"WARC-Payload-Digest\":\"sha1:TOJLXNQHSM4SKYMCYIQIDF2ZTFPDXZCH\",\"WARC-Block-Digest\":\"sha1:G4XWJPIXQUYOUOCH5HLXE3WTC25BQL66\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-05/CC-MAIN-2022-05_segments_1642320304810.95_warc_CC-MAIN-20220125100035-20220125130035-00162.warc.gz\"}"}