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1 + 2P*3Q= Perfect Square (Posted on 2010-03-19) Difficulty: 4 of 5
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    
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Some Thoughts 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   next
OK
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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