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

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

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

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: 2
config / split: AIME2025-I / test

Official source

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