Perfect Totient Number
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. More generally if p is a prime number greater than three, and 3p is a perfect totient number, then p 1 (mod 4) (Mohan and Suryanarayana 1982). Not all p of this form lead to perfect totient numbers; for instance, 51 is not a perfect totient number. Iannucci et al. (2003) showed that if 9p is a perfect totient number then p is a prime of one of three specific forms listed in their paper. It is not known whether there are any perfect totient numbers that are multiples o...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. More generally if p is a prime number greater than three, and 3p is a perfect totient number, then p 1 (mod 4) (Mohan and Suryanarayana 1982). Not all p of this form lead to perfect totient numbers; for instance, 51 is not a perfect totient number. Iannucci et al. (2003) showed that if 9p is a perfect totient number then p is a prime of one of three specific forms listed in their paper. It is not known whether there are any perfect totient numbers that are multiples of powers of 3 greater than 9 but not themselves powers of three.
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