MathDB

Steve says to Jon, "I am thinking of a polynomial whose roots are all positive integers. The polynomial has the form

P(x)=2x^3-2ax^2+(a^2-81)x-c

for some positive integers

a

and

c

. Can you tell me the values of

a

and

c

?"
After some calculations, Jon says, "There is more than one such polynomial."
Steve says, "You’re right. Here is the value of

a

." He writes down a positive integer and asks, "Can you tell me the value of

c

?"
Jon says, "There are still two possible values of

c

."
Find the sum of the two possible values of

c

Problem Statement