1967 IMO Problems/Problem 5
Let be reals, not all equal to zero. Let for . Given that among the numbers of the sequence , there are infinitely many equal to zero, determine all the values of for which
It can be found here 
Problem 5 on this (https://artofproblemsolving.com/wiki/index.php/1967_IMO_Problems) page is equivalent to this since the only difference is that they are phrased differently.