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Omni-MATH / Given that a,b,c are integers with abc=60, and that complex number ω≠1 satisfies ω³=1, find the minimum possible value of |a+bω+cω²|.

Problem

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problem

Given that a,b,ca, b, c are integers with abc=60a b c=60, and that complex number ω≠1\omega \neq 1 satisfies ω3=1\omega^{3}=1, find the minimum possible value of |a+bω+cω2|\left|a+b \omega+c \omega^{2}\right|.
Plain-text mathematical notation (without MathML)
Given that a,b,c are integers with abc=60, and that complex number ω≠1 satisfies ω³=1, find the minimum possible value of |a+bω+cω²|.
Original LaTeX notation
Given that $a, b, c$ are integers with $a b c=60$, and that complex number $\omega \neq 1$ satisfies $\omega^{3}=1$, find the minimum possible value of $\left|a+b \omega+c \omega^{2}\right|$.

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Source and history

task_id
0de25130-3c9a-576c-848f-8f85b9200abe
task_key
test--0de25130-3c9a-576c-848f-8f85b9200abe
task_revision_id
1
config / split
/ test

Official source

initial import