
#1
Nov1812, 12:36 PM

P: 250

let P(n) = n^4 + an^3 + bn^2 + cn
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. 



#2
Nov1812, 02:01 PM

Mentor
P: 10,840

If m divides P(n) for all n, it also divides all differences: m divides P(2)P(1) = 15+7a+3b, for example.
Using more values for n, you can eliminate more variables. This could help to reduce testing. 


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