The product (1+x+x^2+x^3+...)(1+x^3+x^6+x^9+...)(1+x^5+x^10+.. .)... is the generating function for the number of partitions of n into odd parts.
How can you replace some of the plus signs with minus signs so that the resulting product when expanded has coefficients which are all either +1, zero, or -1?
(There are many solutions.)