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PX + 144 = Perfect Square (Posted on 2010-01-12) Difficulty: 3 of 5
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    
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Solution 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   next
OK
run
 2  5    25      13  169
 4  3    81      15  225
 8  2    256     20  400
Overflow in 60
?tot
 1318
OK
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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