How do I prove my Carmichael number?
A composite integer n is a Carmichael number if and only if an ≡ a mod n for all a ∈ Z. Proof. If an ≡ a mod n for all a ∈ Z, then when (a, n) = 1 we can cancel a from both sides and get an-1 ≡ 1 mod n, so n is a Carmichael number since it is composite.
Is 1729 a Carmichael number?
The first few Carmichael numbers are 561, 1105, 1729, 2465, 2821, 6601 and 8911.
IS 561 is a Carmichael number?
3. Hence, 561 is a Carmichael number, because it is composite and b560 ≡ (b80)7 ≡ 1 mod 561 for all b relatively prime to 561. for all b relatively prime to 1105.
Is 1103 a Carmichael number?
The first Quasi–Carmichael numbers are: 35, 77, 143, 165, 187, 209, 221, 231, 247, 273, 299, 323, 357, 391, 399, 437, 493, 527, 561, 589, 598, 713, 715, 899, 935, 943, 989, 1015, 1073, 1105, 1147, 1189, 1247, 1271, 1295, 1333, 1517, 1537, 1547, 1591, 1595, 1705, 1729.
Which of the following is a Carmichael number?
Alford, W. R.; Granville, A.; and Pomerance, C. “There are Infinitely Many Carmichael Numbers.” Ann. Math. 139, 703-722, 1994….Carmichael Number.
| factors | digits | discoverer |
|---|---|---|
| 6 | 19140 | Broadhurst 2003 (Broadhurst 2015a) |
How is Carmichael calculated?
Carmichael Number Tool for testing and calculating Carmichael numbers. A Carmichael number (also called an strong pseudo-prime number) is a number N such as A^(N-1) ≡ 1 mod N for all integer A.
Is 62745 a Carmichael number?
The Fermat probable primality test will fail to show a Carmichael number is composite until we run across one of its factors! The Carmichael numbers under 100,000 are. 561, 1105, 1729, 2465, 2821, 6601, 8911, 10585, 15841, 29341, 41041, 46657, 52633, 62745, 63973, and 75361.
Is 22 a Smith number?
Mathematical definition The first few Smith numbers in base 10 are: 4, 22, 27, 58, 85, 94, 121, 166, 202, 265, 274, 319, 346, 355, 378, 382, 391, 438, 454, 483, 517, 526, 535, 562, 576, 588, 627, 634, 636, 645, 648, 654, 663, 666, 690, 706, 728, 729, 762, 778, 825, 852, 861, 895, 913, 915, 922, 958, 985, 1086 …
Is 2821 a Carmichael number?
, we have then shown that 2821 is a Carmichael number.
What number is Kaprekar?
6174
6174 is known as Kaprekar’s constant after the Indian mathematician D. R. Kaprekar. This number is notable for the following rule: Take any four-digit number, using at least two different digits (leading zeros are allowed).
What is Kaprekar number in Java?
A Kaprekar number for a given base is a non-negative integer, the representation of whose square in that base can be split into two parts that add up to the original number again. For instance, 45 is a Kaprekar number, because 452 = 2025 and 20+25 = 45.
What is Smith number in Java?
A composite number whose sum of digits equal to the sum of the digits of its prime factors.