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MATH / It is given that log₆a+log₆b+log₆c=6, where a, b, and c are positive integers that form an increasing geometric sequence and b−a is the square of an integer. Find a+b+c.

Problem

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problem

It is given that log6a+log6b+log6c=6\log_{6}a + \log_{6}b + \log_{6}c = 6, where aa, bb, and cc are positive integers that form an increasing geometric sequence and b−ab - a is the square of an integer. Find a+b+ca + b + c.
Plain-text mathematical notation (without MathML)
It is given that log₆a+log₆b+log₆c=6, where a, b, and c are positive integers that form an increasing geometric sequence and b−a is the square of an integer. Find a+b+c.
Original LaTeX notation
It is given that $\log_{6}a + \log_{6}b + \log_{6}c = 6$, where $a$, $b$, and $c$ are positive integers that form an increasing geometric sequence and $b - a$ is the square of an integer. Find $a + b + c$.

level

Level 4

type

Intermediate Algebra

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Source and history

task_id
7a903c7f-28ac-50af-94c9-910151ac8120
task_key
intermediate~5falgebra--test--7a903c7f-28ac-50af-94c9-910151ac8120
task_revision_id
1
config / split
intermediate_algebra / test

Official source

initial import