Geodesic
On the exponents of non-trivial divisors of odd numbers and a generalization of Proth's primality theorem
Journal of integer sequences, Tome 20 (2017) no. 2
We present a family of integer sequences characterizing the behavior of the quotients $\sigma /s$ for a given odd natural number $H$, where $N = H ; 2^{\sigma } + 1$ is a composite number and $h ; 2^{s} + 1 (h \ge 1$ odd, $s, \sigma \in $ N) is a non-trivial divisor of $N$. As an application we prove a generalization of the primality theorem of Proth.
Classification : 11A41, 11A51, 11B83, 11D61, 11D72, 11Y11
Keywords: exponent, non-trivial divisor, composite number, primality test, prime number, Diophantine equation, generalized Fermat number, Fermat period 
@article{JIS_2017__20_2_a5,
     author = {M\"uller,  Tom},
     title = {On the exponents of non-trivial divisors of odd numbers and a generalization of {Proth's} primality theorem},
     journal = {Journal of integer sequences},
     year = {2017},
     volume = {20},
     number = {2},
     zbl = {1425.11012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2017__20_2_a5/}
}
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Müller,  Tom. On the exponents of non-trivial divisors of odd numbers and a generalization of Proth's primality theorem. Journal of integer sequences, Tome 20 (2017) no. 2. http://geodesic.mathdoc.fr/item/JIS_2017__20_2_a5/