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Given that m - 2 is a positive integer that divides 3m^2 - 2m + 11, find the sum of all such values of m.

 Apr 13, 2022
 #1
avatar+122 
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"Given that m - 2 is a positive integer that divides 3m^2 - 2m + 11, find the sum of all such values of m."

 

 

For the last term to be an integer we must have m - 2 = 1, so m = 3;  or  m - 2 = 19, so m = 21

 

Hence sum = 3 + 21 = 24

 Apr 13, 2022
 #2
avatar+117180 
+1

Thanks Kakahi,    laugh

 

I just want to look for myself   frown

Given that m - 2 is a positive integer that divides 3m^2 - 2m + 11, find the sum of all such values of m.

 

f(m)=3m^2 - 2m + 11

f(2)=12-4+11 = 19    that is the remainder/

19 is prime

19/(m-2) must be a whole number

m-2=19    or m-2=1

m=21     or   m=3

 

Just like  Kakashi said :)   cool

 Apr 14, 2022

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