Viewing a polynomial's integer values

Question

I'm working on a project that requires polynomials meeting at integers. I currently need a polynomial that goes through the point (70,302), has a degree above 4, and has at least one other point between y= 0-300, where both x and y are integer values. I was wondering if there was some mathematical formula for solving this problem. 

Answer 1

Tyler,

        The problem you pose is "under constrained" a fifth order polynomial has six constants five coefficients and one constant term. So in general you would need at least five more points. However you could assume y=kx⁵+b and least square fit this to (70,302) and say (50,200). This would satisfy your all the conditions.

 

Hope this helps

 

Jim