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 PX + 144 = Perfect Square (Posted on 2010-01-12)
X is a positive integer > 1 and, P is a prime number. Determine all possible pairs (X, P) such that PX + 144 is a perfect square.

 No Solution Yet Submitted by K Sengupta No Rating

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 computer solution | Comment 5 of 9 |
`list   10   for Tot=1 to 999999   20   for X=2 to Tot-2   30      P=Tot-X   40      if prmdiv(P)=P then   50        :Sq=P^X+144   60        :Sr=int(sqrt(Sq)+0.5)   70        :if Sr*Sr=Sq then print X;P,P^X,Sr;Sq   80   next   90   nextOKrun 2  5    25      13  169 4  3    81      15  225 8  2    256     20  400Overflow in 60?tot 1318OK`
`So the three solutions are all there are for p+x < 1318.`
` x  p   p^x  sqrt(p^x+144) p^x+144 2  5    25      13         169 4  3    81      15         225 8  2    256     20         400`

 Posted by Charlie on 2010-01-12 13:03:50

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