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2027 divides

Source: 2024 Indonesia Regional MO Essay Problem 4

May 6, 2024
number theoryQuadratic Residuesquadratic reciprocityIndonesiaRMO

Problem Statement

Find the number of positive integer pairs 1⩽a,b⩽20271\leqslant a,b \leqslant 2027 that satisfy 2027∣a6+b5+b2 2027 \mid a^6+b^5+b^2 (Note: For integers aa and bb, the notation a∣ba \mid b means that there is an integer cc such that ac=bac=b)
Proposed by Valentio Iverson, Indonesia
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