Benchmark AI / Public workspace
OlympiadBench / 1929 / Find all pairs (m,n) of positive integers satisfying the equation
Problem
Answer published by the source. Consult the official source to check your work against its answer.
answer type
Tuple
is multiple answer
true
language
English
question
Find all pairs of positive integers satisfying the equation
$$
\left(2^{n}-1\right)\left(2^{n}-2\right)\left(2^{n}-4\right) \cdots\left(2^{n}-2^{n-1}\right)=m !
\tag{1}
$$Plain-text mathematical notation (without MathML)
Find all pairs (m,n) of positive integers satisfying the equation
$$
\left(2^{n}-1\right)\left(2^{n}-2\right)\left(2^{n}-4\right) \cdots\left(2^{n}-2^{n-1}\right)=m !
\tag{1}
$$Original LaTeX notation
Find all pairs $(m, n)$ of positive integers satisfying the equation
$$
\left(2^{n}-1\right)\left(2^{n}-2\right)\left(2^{n}-4\right) \cdots\left(2^{n}-2^{n-1}\right)=m !
\tag{1}
$$question type
Open-ended
subject
Math
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