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 1 + 2P*3Q= Perfect Square (Posted on 2010-03-19)
Determine all possible pair(s) (P, Q) of nonnegative integers such that 1 + 2P*3Q is a perfect square.

 No Solution Yet Submitted by K Sengupta No Rating

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 computer exploration Comment 1 of 1

Up to the point where the sum of p and q reaches 5391, there are only 5 sets of (p,q).

`list   10   for Sum=1 to 10000000   20     for P=0 to Sum   30        Q=Sum-P   40        V=1+2^P*3^Q   50        Sr=int(sqrt(V)+0.5)   60        if Sr*Sr=V then print P,Q,V,Sr   70     next   80   nextOK`
`produces      `
` p       q   1+2^P*3^Q  sqrt(1+2^P*3^Q) 0       1         4           2 3       0         9           3 3       1        25           5 4       1        49           7 5       2       289          17 `

before overflowing at a sum of p and q equal to 5391.

 Posted by Charlie on 2010-03-19 12:58:28

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