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2024 KJMO P6 find all pairs

Source: 2024 KJMO P6

November 9, 2024

number theoryprime numbers

Problem Statement

Find all pairs

(n, p)

that satisfy the following condition, where

n

is a positive integer and

p

is a prime number.
Condition)

2n-1

is a divisor of

p-1

and

p

is a divisor of

4n^2+7

.

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