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.
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
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Posted by Charlie
on 2010-01-12 13:03:50 |
computer solution
