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AIME 2024 / AIME 2024 train de893695-bb70-5ca2-a09d-5b1876197ee0

Problem

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

Problem

Find the number of triples of nonnegative integers

(a,b,c)

satisfying

a + b + c = 300

and

a^2b + a^2c + b^2a + b^2c + c^2a + c^2b = 6,000,000.

Plain-text mathematical notation (without MathML)

Find the number of triples of nonnegative integers (a,b,c) satisfying a+b+c=300 and a²b+a²c+b²a+b²c+c²a+c²b=6,000,000.

Original LaTeX notation

Find the number of triples of nonnegative integers $(a,b,c)$ satisfying $a + b + c = 300$ and \[a^2b + a^2c + b^2a + b^2c + c^2a + c^2b = 6,000,000.\]

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Source and history

task_id: de893695-bb70-5ca2-a09d-5b1876197ee0
task_key: default--train--de893695-bb70-5ca2-a09d-5b1876197ee0
task_revision_id: 2
config / split: default / train

Official source

initial import