MathDB

6

Part of 1992 Romania Team Selection Test

Problems(1)

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

Source: Romania IMO TST 1992 p6

2/19/2020
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.
number theoryprimeInteger Polynomialprime numbers