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Omni-MATH / Let N be the number of triples of positive integers (a,b,c) satisfying a≤b≤c, gcd(a,b,c)=1, abc=6²⁰²⁰. Compute the remainder when N is divided by 1000.

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problem

Let NN be the number of triples of positive integers (a,b,c)(a, b, c) satisfying a≤b≤c,gcd(a,b,c)=1,abc=62020a \leq b \leq c, \quad \operatorname{gcd}(a, b, c)=1, \quad a b c=6^{2020}. Compute the remainder when NN is divided by 1000.
Plain-text mathematical notation (without MathML)
Let N be the number of triples of positive integers (a,b,c) satisfying a≤b≤c, gcd(a,b,c)=1, abc=6²⁰²⁰. Compute the remainder when N is divided by 1000.
Original LaTeX notation
Let $N$ be the number of triples of positive integers $(a, b, c)$ satisfying $a \leq b \leq c, \quad \operatorname{gcd}(a, b, c)=1, \quad a b c=6^{2020}$. Compute the remainder when $N$ is divided by 1000.

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Source and history

task_id
346de1cd-9c24-5e25-bd4c-1b2d6161bfb9
task_key
test--346de1cd-9c24-5e25-bd4c-1b2d6161bfb9
task_revision_id
1
config / split
/ test

Official source

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