Let m be a "whoo-whee number" if there exist 4 polynomials A(x), B(x), C(x), D(x) with degree(A)=degree(B)=m, degree(C)=degree(D)=m+1, all coefficients in all polynomials +-1, and A(x)A(1/x)+B(x)B(1/x)+C(x)C(1/x)+D(x)D(1/x) = 4m+6. Note the right hand side does not depend on x, so we are asking for a lot of cancellation here. I can show there are an infinite set of whoo-whee numbers. Computers seem to think every number is a whoo-whee number (at least as far out as computers can see). THE (UNSOLVED) PROBLEM: prove the count of whoo-whee numbers below X ultimately grows at least like some positive power of X, for example X^0.001. Ideas welcome even if not solutions. This is an example of a frustrating combinatorial construction problem where the gulf between what seems true (all numbers) and what I can prove (a very sparse set of numbers) is enormous, but it might not be hard to break the impasse. Warren D. Smith warren.wds AT gmail.com