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math.NT2009
On integers as the sum of a prime and a -th power
Aran Nayebi
Let be the number of representations of an integer as the sum of a prime and a -th power. Define E_k(X) := |\{n \le X, n \in I_k, n\text{not a sum of a pr…
math.NT2009
On the distribution of Carmichael numbers
Aran Nayebi
Erdős conjectured in 1956 that there are Carmichael numbers up to . Pomerance made this conjecture more precise and proposed that there are $x^{1-{\frac{\{1+o(1)\}\…