Find an effective way to determine whether a polynomial equation with integer coefficients and one or more unknowns has any integer solutions. (Sort of like the quadratic formula.)
I never went beyond elementary calculus, and didn't learn that very well. But I can sort of vaguely see how solving this would be both beautiful and spooky. 3x*4 + 7y*3 + 13y - 17x - 7xy - 374 = 0 If I understand this correctly, what is sought is a method by which one could, just by inspecting this equation, but without solving it, determine whether or not it held for some values of x & y as whole numbers!!! And if, as is often the case with mathematical discoveries, it was then found that this method illuminated physical relations not recognized or understood before. I really wish I'd had two or three more years of math. Carrol
