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Old 2020-04-04, 05:47   #1
devarajkandadai's Avatar
May 2004

22·79 Posts
Default 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 = N'*P_1*P_2 is a Carmichael number subject to Korselt's criterion
Examples: 1729*8641*19009 = 283999953601
1729*19009*103681 = 3407637911041

2821*5641*8461 = 134642101321

Remarks a) note the first factor is a Carmichael number; the number on the right side of each equation is also a Carmichael number

b) not only does N satisfy Korselt's criterion but also extended Korselt's criterion I.e. (N -1) is divisible by (N' -1)
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