Let α ∈ ℤ\{0}. A composite number N is said to be an α-Korselt number (Kα-number, for short) if N ≠ α and p - α divides N - α for each prime divisor p of N. The set of all α ∈ ℤ\{0} such that N is a Kα-number is called the Korselt set of N and is denoted by 𝒦𝒮(N). In this paper, we study the Korselt set of q2, where q is prime. We describe in detail how to obtain 𝒦𝒮(q2), compute the cardinality of 𝒦𝒮(q2), and answer some questions related to 𝒦𝒮(q2).

Let D be an integral domain with quotient field K. A Bhargava ring over D is defined to be x D = f ∈ K X ∀a ∈ D f xX + a ∈ D X , where x ∈ D. A Bhargava ring over D is a subring of the ring of integer-valued polynomials over D. In this article, we study the prime ideal structure and calculate the Krull and valuative dimension of Bhargava rings over a general domain D.

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