MathDB

6

Part of 2024 Korea Junior Math Olympiad

Problems(1)

2024 KJMO P6 find all pairs

Source: 2024 KJMO P6

11/9/2024
Find all pairs (n,p)(n, p) that satisfy the following condition, where nn is a positive integer and pp is a prime number.
Condition) 2n−12n-1 is a divisor of p−1p-1 and pp is a divisor of 4n2+74n^2+7.
number theoryprime numbers