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 Showing results 1 to 25 of 316 Search took 0.05 seconds. Search: Posts Made By: devarajkandadai
 Forum: Miscellaneous Math 2020-07-18, 09:13 Replies: 1 Views: 2,954 Posted By devarajkandadai Group theory How come there is a number theory discussion group but no group theory discussion group?
 Forum: Miscellaneous Math 2020-07-18, 09:04 Replies: 57 Views: 26,631 Posted By devarajkandadai Recall that Taylor's theorem can be stated as ... Recall that Taylor's theorem can be stated as f(x+h) =f(x) + hf'(x)..h^2/2!f''(x)...... Just replace h by f(x) and you get the required proof.
 Forum: Miscellaneous Math 2020-07-16, 04:36 Replies: 57 Views: 26,631 Posted By devarajkandadai Ok so I have been hasty.here is a summary of my... Ok so I have been hasty.here is a summary of my contributions to number theory: Euler's generalization of Fermat's theorem- a further generalization (ISSN #1550 3747- Hawaii international...
 Forum: Miscellaneous Math 2020-07-14, 04:33 Replies: 57 Views: 26,631 Posted By devarajkandadai This example is not correct.correct example: 23... This example is not correct.correct example: 23 is non-residue of 3571 upto infinite order.I leave it to pari experts like Charles to verify.
 Forum: Miscellaneous Math 2020-07-13, 13:55 Replies: 57 Views: 26,631 Posted By devarajkandadai A tentative question Sorry;just proved that 23 is a non-residue of 7919 upto infinite order. This was done with aid of my paper "Euler's generalization of Fermat's theorem ( a further generalization)- Hawaii...
 Forum: Miscellaneous Math 2020-07-13, 13:23 Replies: 57 Views: 26,631 Posted By devarajkandadai A tentative question Sorry;just proved that 23 is a non-residue of 7919 upto infinite order. This was done with aid of my paper "Euler's generalization of Fermat's theorem ( a further generalization)- Hawaii...
 Forum: Miscellaneous Math 2020-07-13, 07:05 Replies: 3 Views: 2,564 Posted By devarajkandadai Thanks.Are they all 2 stringed ellipses? Thanks.Are they all 2 stringed ellipses?
 Forum: Miscellaneous Math 2020-07-10, 04:26 Replies: 57 Views: 26,631 Posted By devarajkandadai A tentative question There seems to be no non-residues higher than quadratic order;is this related to Fermat's last theorem?
 2020-04-04, 05:47 Replies: 0 Views: 4,868 Posted By devarajkandadai A new type of Carmichael number A special type of Carmichael number: Let N' =p_1*p_2*p_3 be a 3 -prime factor Carmichael number Now form two primes having form K*(N'-1)+1; here k is a natural number.Call them P_1 and P_2 Then N...
 2020-02-02, 04:34 Replies: 2 Views: 5,356 Posted By devarajkandadai Algorithm for generating Carmichael numbers of type 1105 1) Let n be = = 1 (mod 3) 2)check whether n satisfying above is such that (4n+1), (12n+1) and (16n+1) are primes. If so N = (4n+1)(12n+1)(16n+1) is a Carmichael number of type 1105.
 Forum: Miscellaneous Math 2020-01-31, 12:39 Replies: 3 Views: 2,564 Posted By devarajkandadai Elliptic Carmichael numbers I had a conjecture that the above (defined below) exist. A set of 2 or more Carmichael numbers in which the smallest and largest prime factors are common but the intervening prime factors are...
 2019-09-24, 03:14 Replies: 2 Views: 4,297 Posted By devarajkandadai Another set of spiral Carmichael numbers: 252601... Another set of spiral Carmichael numbers: 252601 = 41*61*101 151813201 = 41*61*101*601 182327654401=41*61*101*601*1201 875355068779201 = 41*61*101*601*1201*4801* 12605988345489273601 =...
 2019-09-21, 05:40 Replies: 1 Views: 4,704 Posted By devarajkandadai Just combined 3 Carmichael numbers to form one... Just combined 3 Carmichael numbers to form one Carmichael number; all three are of type (6m+1)(12m+1)(18m+1). 1729*294409*118901521 =60524817082337881. Conjecture: There can be many Carmichael...
 2019-09-14, 13:11 Replies: 1 Views: 4,704 Posted By devarajkandadai Algorithm for combining Carmichael numbers We can combine two Carmichael numbers to form another Carmichael number. An example: 1729 = 7*13*19 294409 = 37*73*109 Both are of type (6m+1)(12m+1)(18m+1); we get the...
 2019-09-05, 10:43 Replies: 0 Views: 3,430 Posted By devarajkandadai Another generalisation of Euler's generalisation of Fermat's theorem Let x be a Gaussian integer. Then ((x-1)^(k*eulerphi(norm of x)-1) is congruent to 0 (mod x). Here k belongs to N.
 Forum: Miscellaneous Math 2019-08-26, 04:13 Replies: 2 Views: 1,006 Posted By devarajkandadai Complex Devaraj numbers Recall that if N = p_1*p_2....p_r and if ((P_1-1)*(N-1)^(r-2)/((p_2-1)… (p_r-1)) is an integer then N is a Devaraj number. Q: are there complex Devaraj numbers? Yes here is an...
 2019-08-13, 04:43 Replies: 2 Views: 4,297 Posted By devarajkandadai Another set of continued product Carmichael... Another set of continued product Carmichael numbers ( prefer to call them "spiral Carmichael numbers"): a)2821 = 7*13* 31 b)172081= 7*13*31*61 ...
 2019-08-11, 05:01 Replies: 2 Views: 4,297 Posted By devarajkandadai Continued product Carmichael numbers Let me give an example of a set of continued product Carmichael numbers: a)2465 = 5*17*29 b)278545 = 5*17*29*113 c)93969665=5*17*29*113*337 d)63174284545 = 5*17*29*113*337*673 and...
 2019-04-20, 05:47 Replies: 1 Views: 4,535 Posted By devarajkandadai 2) one implies many: I.e. if a zero exists on... 2) one implies many: I.e. if a zero exists on any line parallel to 1/2 then many ought to exist. If this can be proved we have practicality proved RH.
 2019-04-19, 11:54 Replies: 1 Views: 4,535 Posted By devarajkandadai Random thoughts on RH 1) We can say that proving RH is equivalent to proving that zeta(s + it) is a non trivial non-zero when the real part (s) is other than 1/2, irrespective of the imaginary part(t) (to be...
 2018-12-01, 06:44 Replies: 14 Views: 6,209 Posted By devarajkandadai C) let N = (2*m+1)*(10*m+1)*(16*m+1)- here m is a... C) let N = (2*m+1)*(10*m+1)*(16*m+1)- here m is a natural nnumber. Then N is a Carmichael number if a) for a given value of m, 2*m+1, 10*m+1 and 16*m+1 are prime and b) 80*m^2 + 53*m + 7 is exactly...
 2018-11-10, 05:17 Replies: 1 Views: 2,292 Posted By devarajkandadai P-adic inverses It seems that, r, the number of prime factors of a Carmichael number is conjectured to be not bounded. The two conjectures (that pertaining to k and that pertaining to r may be related I.e. if one...
 2018-11-08, 05:28 Replies: 1 Views: 2,292 Posted By devarajkandadai P-adic inverses The concept of higher degree inverses has already been introduced in thread: a tentative definition. Conjecture: k, the degree of inverse of p, a prime number, is not bounded.
 2018-11-05, 04:16 Replies: 14 Views: 6,209 Posted By devarajkandadai 175129 and 3403470857219 are inverses of degree... 175129 and 3403470857219 are inverses of degree 25 (mod 5^25)
 2018-11-04, 05:30 Replies: 14 Views: 6,209 Posted By devarajkandadai Carmichael numbers and Devaraj numbers 41and 61 are inverses of degree 4 (mod 5^4). 17 and 6947 are inverses of degree 10 (mod 3^10).
 Showing results 1 to 25 of 316

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