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Omni-MATH / Find a nonzero polynomial P(x,y) such that P(⌊a⌋,⌊2a⌋)=0 for all real numbers a. (Note: ⌊ν⌋ is the greatest integer less than or equal to ν.)

Problem

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problem

Find a nonzero polynomial P(x,y)P(x,y) such that P(⌊a⌋,⌊2a⌋)=0P(\lfloor a \rfloor, \lfloor 2a \rfloor) = 0 for all real numbers aa. (Note: ⌊ν⌋\lfloor \nu \rfloor is the greatest integer less than or equal to ν\nu.)
Plain-text mathematical notation (without MathML)
Find a nonzero polynomial P(x,y) such that P(⌊a⌋,⌊2a⌋)=0 for all real numbers a. (Note: ⌊ν⌋ is the greatest integer less than or equal to ν.)
Original LaTeX notation
Find a nonzero polynomial $P(x,y)$ such that $P(\lfloor a \rfloor, \lfloor 2a \rfloor) = 0$ for all real numbers $a$. (Note: $\lfloor \nu \rfloor$ is the greatest integer less than or equal to $\nu$.)

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Source and history

task_id
8d6efd87-fb8d-5784-861c-3900d66364a3
task_key
test--8d6efd87-fb8d-5784-861c-3900d66364a3
task_revision_id
1
config / split
/ test

Official source

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