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Forum: Miscellaneous Math 2020-07-18, 09:13
Replies: 1
Views: 456
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: 3,436
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: 3,436
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: 3,436
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: 3,436
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: 3,436
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: 1,054
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: 3,436
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?
Forum: Number Theory Discussion Group 2020-04-04, 05:47
Replies: 0
Views: 873
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...
Forum: Number Theory Discussion Group 2020-02-02, 04:34
Replies: 2
Views: 870
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: 1,054
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...
Forum: Number Theory Discussion Group 2019-09-24, 03:14
Replies: 2
Views: 965
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 =...
Forum: Number Theory Discussion Group 2019-09-21, 05:40
Replies: 1
Views: 736
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...
Forum: Number Theory Discussion Group 2019-09-14, 13:11
Replies: 1
Views: 736
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...
Forum: Number Theory Discussion Group 2019-09-05, 10:43
Replies: 0
Views: 756
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: 381
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...
Forum: Number Theory Discussion Group 2019-08-13, 04:43
Replies: 2
Views: 965
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
...
Forum: Number Theory Discussion Group 2019-08-11, 05:01
Replies: 2
Views: 965
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...
Forum: Number Theory Discussion Group 2019-04-20, 05:47
Replies: 1
Views: 815
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.
Forum: Number Theory Discussion Group 2019-04-19, 11:54
Replies: 1
Views: 815
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...
Forum: Number Theory Discussion Group 2018-12-01, 06:44
Replies: 14
Views: 1,572
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...
Forum: Number Theory Discussion Group 2018-11-10, 05:17
Replies: 1
Views: 622
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...
Forum: Number Theory Discussion Group 2018-11-08, 05:28
Replies: 1
Views: 622
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.
Forum: Number Theory Discussion Group 2018-11-05, 04:16
Replies: 14
Views: 1,572
Posted By devarajkandadai
175129 and 3403470857219 are inverses of degree...

175129 and 3403470857219 are inverses of degree 25 (mod 5^25)
Forum: Number Theory Discussion Group 2018-11-04, 05:30
Replies: 14
Views: 1,572
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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