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Cube*Linear = Square*Cube (Posted on 2008-08-09) Difficulty: 2 of 5
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.

No Solution Yet Submitted by K Sengupta    
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Some Thoughts trivial solution Comment 1 of 1

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
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