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Number of integer pair

Source: 2017 Korea Winter Program Practice Test 2 #5

August 14, 2019
number theory

Problem Statement

Find all prime number pp such that the number of positive integer pair (x,y)(x,y) satisfy the following is not 2929.
[*]1≤x,y≤291\le x,y\le 29 [*]29∣y2−xp−2629\mid y^2-x^p-26
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