Determine all possible positive integer pair(s) (P, Q) that satisfy this equation.

P³(3P+1) = Q²(Q+1)³.

Bonus Question:

What are the possible positive integer pair(s) (R, S) that satisfy this equation?

R³(4R+1) = S²(S+1)³.

if p=q+1 and  q^2=3p+1

q^2-3q-4=0

leading to two trivial answers:    q=4   p=5 

and  p=0 q=-1  '( second does not qualify)

bonus : similar reasoning forces  s=5 and r=4

 

I DID NOT ADDRESS EXISTENCE OF OTHER ANSWERS

 

Posted by Ady TZIDON on 2008-08-09 17:06:59