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Omni-MATH / Simplify the product ∏_(m=1)¹⁰⁰∏_(n=1)¹⁰⁰(x^(n+m)+x^(n+m+2)+x^(2n+1)+x^(2m+1))/(x^(2n)+2x^(n+m)+x^(2m)) Express your answer in terms of x.

Problem

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problem

Simplify the product ∏m=1100∏n=1100xn+m+xn+m+2+x2n+1+x2m+1x2n+2xn+m+x2m\prod_{m=1}^{100} \prod_{n=1}^{100} \frac{x^{n+m}+x^{n+m+2}+x^{2 n+1}+x^{2 m+1}}{x^{2 n}+2 x^{n+m}+x^{2 m}} Express your answer in terms of xx.
Plain-text mathematical notation (without MathML)
Simplify the product ∏_(m=1)¹⁰⁰∏_(n=1)¹⁰⁰(x^(n+m)+x^(n+m+2)+x^(2n+1)+x^(2m+1))/(x^(2n)+2x^(n+m)+x^(2m)) Express your answer in terms of x.
Original LaTeX notation
Simplify the product $$\prod_{m=1}^{100} \prod_{n=1}^{100} \frac{x^{n+m}+x^{n+m+2}+x^{2 n+1}+x^{2 m+1}}{x^{2 n}+2 x^{n+m}+x^{2 m}}$$ Express your answer in terms of $x$.

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Source and history

task_id
964b17cc-84d4-5cba-9e88-8dad652d0e2e
task_key
test--964b17cc-84d4-5cba-9e88-8dad652d0e2e
task_revision_id
1
config / split
/ test

Official source

initial import