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Determine all possible positive integer triplet(s) (F, G, H) such that each of F and G is a prime with FG, and:

F(F+3) + G(G+3) = H(H+3)

 See The Solution Submitted by K Sengupta Rating: 3.0000 (1 votes)

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 computer exploration (probable spoiler) | Comment 1 of 6

The following UBASIC program was interrupted when the total of possible F and G was up to 239,285, and so the solutions found

(2,       3,       4)
(3,       7,       8)

are the only ones where F and G add up to less than 239,285.

`list   10   for Tot=1 to 1000000   20          F=2   30          while F<=Tot/2   40           G=Tot-F   50           if prmdiv(G)=G then   60            :Lhs=F*(F+3)+G*(G+3)   70            :Disc=9+4*Lhs   80            :Sr=int(sqrt(Disc)+0.5)   90            :if Sr*Sr=Disc then  100             :H=(Sr-3)/2  110             :if H=int(H) then print F,G,H  115           F=nxtprm(F)  120          wend  130    next TotOK`
`run 2       3       4.0 3       7       8.0Break in 80`
`?tot 239285OK`

 Posted by Charlie on 2008-04-19 12:55:35

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