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Problem about Prime

Source: 1996 National High School Mathematics League, Exam One, Problem 3

March 3, 2020
number theoryprime numbers

Problem Statement

For a prime number pp, there exists n∈Z+n\in\mathbb{Z}_+, p+n+n\sqrt{p+n}+\sqrt{n} is an integer, then (A)\text{(A)} there is no such pp (B)\text{(B)} there in only one such pp (C)\text{(C)} there is more than one such pp, but finitely many (D)\text{(D)} there are infinitely many such pp
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