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Omni-MATH / FIx positive integer n. Prove: For any positive integers a,b,c not exceeding 3n²+4n, there exist integers x,y,z with absolute value not exceeding 2n and not all 0, such that …

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problem

FIx positive integer nn. Prove: For any positive integers a,b,ca,b,c not exceeding 3n2+4n3n^2+4n, there exist integers x,y,zx,y,z with absolute value not exceeding 2n2n and not all 00, such that ax+by+cz=0ax+by+cz=0
Plain-text mathematical notation (without MathML)
FIx positive integer n. Prove: For any positive integers a,b,c not exceeding 3n²+4n, there exist integers x,y,z with absolute value not exceeding 2n and not all 0, such that ax+by+cz=0
Original LaTeX notation
FIx positive integer $n$. Prove: For any positive integers $a,b,c$ not exceeding $3n^2+4n$, there exist integers $x,y,z$ with absolute value not exceeding $2n$ and not all $0$, such that $ax+by+cz=0$

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Source and history

task_id
b78dc2f6-628b-59cd-8be9-c72ef6040a2c
task_key
test--b78dc2f6-628b-59cd-8be9-c72ef6040a2c
task_revision_id
1
config / split
/ test

Official source

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