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Omni-MATH / Each of a,b and c is equal to a number from the list 3¹,3²,3³,3⁴,3⁵,3⁶,3⁷,3⁸. There are N triples (a,b,c) with a≤b≤c for which each of (ab)/(c),(ac)/(b) and (bc)/(a) is equal to an…

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problem

Each of a,ba, b and cc is equal to a number from the list 31,32,33,34,35,36,37,383^{1}, 3^{2}, 3^{3}, 3^{4}, 3^{5}, 3^{6}, 3^{7}, 3^{8}. There are NN triples (a,b,c)(a, b, c) with a≤b≤ca \leq b \leq c for which each of abc,acb\frac{ab}{c}, \frac{ac}{b} and bca\frac{bc}{a} is equal to an integer. What is the value of NN?
Plain-text mathematical notation (without MathML)
Each of a,b and c is equal to a number from the list 3¹,3²,3³,3⁴,3⁵,3⁶,3⁷,3⁸. There are N triples (a,b,c) with a≤b≤c for which each of (ab)/(c),(ac)/(b) and (bc)/(a) is equal to an integer. What is the value of N?
Original LaTeX notation
Each of $a, b$ and $c$ is equal to a number from the list $3^{1}, 3^{2}, 3^{3}, 3^{4}, 3^{5}, 3^{6}, 3^{7}, 3^{8}$. There are $N$ triples $(a, b, c)$ with $a \leq b \leq c$ for which each of $\frac{ab}{c}, \frac{ac}{b}$ and $\frac{bc}{a}$ is equal to an integer. What is the value of $N$?

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task_id
d0717168-910a-58c9-be7a-0444ce80a003
task_key
test--d0717168-910a-58c9-be7a-0444ce80a003
task_revision_id
1
config / split
/ test

Official source

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