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Omni-MATH / Find all positive integers n for which there exist positive integers x₁,x₂,…,x_(n) such that (1)/(x₁²)+(2)/(x₂²)+(2²)/(x₃²)+⋯+(2^(n−1))/(x_(n)²)=1.

Problem

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problem

Find all positive integers nn for which there exist positive integers x1,x2,…,xnx_1, x_2, \dots, x_n such that 1x12+2x22+22x32+⋯+2n−1xn2=1. \frac{1}{x_1^2}+\frac{2}{x_2^2}+\frac{2^2}{x_3^2}+\cdots +\frac{2^{n-1}}{x_n^2}=1.
Plain-text mathematical notation (without MathML)
Find all positive integers n for which there exist positive integers x₁,x₂,…,x_(n)  such that 
(1)/(x₁²)+(2)/(x₂²)+(2²)/(x₃²)+⋯+(2^(n−1))/(x_(n)²)=1.
Original LaTeX notation
Find all positive integers $n$ for which there exist positive integers $x_1, x_2, \dots, x_n$  such that 
$$ \frac{1}{x_1^2}+\frac{2}{x_2^2}+\frac{2^2}{x_3^2}+\cdots +\frac{2^{n-1}}{x_n^2}=1.$$

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Source and history

task_id
20f90be3-2a7e-522c-94d9-435aff99d279
task_key
test--20f90be3-2a7e-522c-94d9-435aff99d279
task_revision_id
1
config / split
/ test

Official source

initial import