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Omni-MATH / Mark writes the expression √(d) for each positive divisor d of 8 ! on the board. Seeing that these expressions might not be worth points on HMMT, Rishabh simplifies each expression…

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problem

Mark writes the expression d\sqrt{d} for each positive divisor dd of 8 ! on the board. Seeing that these expressions might not be worth points on HMMT, Rishabh simplifies each expression to the form aba \sqrt{b}, where aa and bb are integers such that bb is not divisible by the square of a prime number. Compute the sum of a+ba+b across all expressions that Rishabh writes.
Plain-text mathematical notation (without MathML)
Mark writes the expression √(d) for each positive divisor d of 8 ! on the board. Seeing that these expressions might not be worth points on HMMT, Rishabh simplifies each expression to the form a√(b), where a and b are integers such that b is not divisible by the square of a prime number. Compute the sum of a+b across all expressions that Rishabh writes.
Original LaTeX notation
Mark writes the expression $\sqrt{d}$ for each positive divisor $d$ of 8 ! on the board. Seeing that these expressions might not be worth points on HMMT, Rishabh simplifies each expression to the form $a \sqrt{b}$, where $a$ and $b$ are integers such that $b$ is not divisible by the square of a prime number. Compute the sum of $a+b$ across all expressions that Rishabh writes.

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Source and history

task_id
01b0c3cb-1483-5297-a6ab-7ef00a1ccff4
task_key
test--01b0c3cb-1483-5297-a6ab-7ef00a1ccff4
task_revision_id
1
config / split
/ test

Official source

initial import