equations in many variables; linear diophantine equations; multiplicative equations; Weierstrass $p$-function; diophantine equations
A proof is given that the system in the title has infinitely many solutions of the form $a_1 + \ii a_2$, where $a_1$ and $a_2$ are rational numbers.
 S. Schwarz: Algebraic Numbers
. Přírodovědecké nakladatelství, Praha, 1950. (In Slovak.) MR 0048500