let P(n) = n^4 + an^3 + bn^2 + cn(adsbygoogle = window.adsbygoogle || []).push({});

M(a,b,c) returns largest m that divides P(n) for all n

then let function S(N) return the sum of all M(a,b,c) for 1 <= a,b,c <= N

I am trying to understand a simpler way to calculate S(N) so I don't have to actually process every single combination of a,b, and c but I am having trouble finding patterns to take advantage of on a broad scale.

So far I know from trying all sorts of values that M(a,b,c) tends to return values of form 2^i * 3^j where i,j>=0.

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Trying to find a simpler way to calculate this function

**Physics Forums | Science Articles, Homework Help, Discussion**