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AIME 2025 I / Find the number of ordered pairs (x,y), where both x and y are integers…

Problem

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question

Find the number of ordered pairs (x,y)(x,y), where both xx and yy are integers between −100-100 and 100100, inclusive, such that 12x2−xy−6y2=012x^{2}-xy-6y^{2}=0.
Plain-text mathematical notation (without MathML)
Find the number of ordered pairs (x,y), where both x and y are integers between −100 and 100, inclusive, such that 12x²−xy−6y²=0.
Original LaTeX notation
Find the number of ordered pairs $(x,y)$, where both $x$ and $y$ are integers between $-100$ and $100$, inclusive, such that $12x^{2}-xy-6y^{2}=0$.

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Source and history

task_id
1f055f8e-78dc-50a6-8fb7-50ef57db44a6
task_key
AIME2025~2dI--test--1f055f8e-78dc-50a6-8fb7-50ef57db44a6
task_revision_id
3
config / split
AIME2025-I / test

Official source

initial import