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Omni-MATH / Find all functions f from the reals to the reals such that (f(x)+f(z))(f(y)+f(t))=f(xy−zt)+f(xt+yz) for all real x,y,z,t.

Problem

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problem

Find all functions ff from the reals to the reals such that (f(x)+f(z))(f(y)+f(t))=f(xy−zt)+f(xt+yz) \left(f(x)+f(z)\right)\left(f(y)+f(t)\right)=f(xy-zt)+f(xt+yz) for all real x,y,z,tx,y,z,t.
Plain-text mathematical notation (without MathML)
Find all functions f from the reals to the reals such that (f(x)+f(z))(f(y)+f(t))=f(xy−zt)+f(xt+yz) for all real x,y,z,t.
Original LaTeX notation
Find all functions $f$ from the reals to the reals such that \[ \left(f(x)+f(z)\right)\left(f(y)+f(t)\right)=f(xy-zt)+f(xt+yz)  \] for all real $x,y,z,t$.

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Source and history

task_id
35a9f772-030b-5e63-a767-e02ec12b9db6
task_key
test--35a9f772-030b-5e63-a767-e02ec12b9db6
task_revision_id
1
config / split
/ test

Official source

initial import