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(7^m + p \cdot 2^n)\(7^m - p \cdot 2^n) is integer then is prime

Source: Romania IMO TST 1992 p6

February 19, 2020
number theoryprimeInteger Polynomialprime numbers

Problem Statement

Let m,nm,n be positive integers and pp be a prime number. Show that if 7m+p⋅2n7m−p⋅2n\frac{7^m + p \cdot 2^n}{7^m - p \cdot 2^n} is an integer, then it is a prime number.
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