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Omni-MATH / The rank of a rational number q is the unique k for which q=(1)/(a₁)+⋯+(1)/(a_(k)), where each a_(i) is the smallest positive integer such that q≥(1)/(a₁)+⋯+(1)/(a_(i)). Let q be t…

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problem

The rank of a rational number qq is the unique kk for which q=1a1+⋯+1akq=\frac{1}{a_{1}}+\cdots+\frac{1}{a_{k}}, where each aia_{i} is the smallest positive integer such that q≥1a1+⋯+1aiq \geq \frac{1}{a_{1}}+\cdots+\frac{1}{a_{i}}. Let qq be the largest rational number less than \frac{1}{4}withrank3,andsupposetheexpressionfor with rank 3, and suppose the expression for qis1a1+1a2+1a3 is \frac{1}{a_{1}}+\frac{1}{a_{2}}+\frac{1}{a_{3}}. Find the ordered triple \left(a_{1}, a_{2}, a_{3}\right).
Plain-text mathematical notation (without MathML)
The rank of a rational number q is the unique k for which q=(1)/(a₁)+⋯+(1)/(a_(k)), where each a_(i) is the smallest positive integer such that q≥(1)/(a₁)+⋯+(1)/(a_(i)). Let q be the largest rational number less than \frac{1}{4}withrank3,andsupposetheexpressionforqis(1)/(a₁)+(1)/(a₂)+(1)/(a₃). Find the ordered triple \left(a_{1}, a_{2}, a_{3}\right).
Original LaTeX notation
The rank of a rational number $q$ is the unique $k$ for which $q=\frac{1}{a_{1}}+\cdots+\frac{1}{a_{k}}$, where each $a_{i}$ is the smallest positive integer such that $q \geq \frac{1}{a_{1}}+\cdots+\frac{1}{a_{i}}$. Let $q$ be the largest rational number less than \frac{1}{4}$ with rank 3, and suppose the expression for $q$ is \frac{1}{a_{1}}+\frac{1}{a_{2}}+\frac{1}{a_{3}}$. Find the ordered triple \left(a_{1}, a_{2}, a_{3}\right).

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Source and history

task_id
d0a10c10-11f1-5314-b50e-2476c6514524
task_key
test--d0a10c10-11f1-5314-b50e-2476c6514524
task_revision_id
1
config / split
/ test

Official source

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