Rado theorem for one equation
= Rado theorem for one equation
{c}
For nonzero rational coefficients $a_1,\ldots,a_n$, the equation
$$
a_1x_1+\cdots+a_nx_n=0
$$
is <partition regular equation>[partition regular] exactly when some nonempty subset of the coefficients has sum zero. This is the one-row form of the <columns property>.