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Sorta pythagoric...(2) (Posted on 2012-05-26) Difficulty: 3 of 5
Given that each of x, y and z is a positive integer, it is observed that the equation 5x + 12y = 13z is satisfied for x=y=z=2.

Does there exist any further solution?

No Solution Yet Submitted by K Sengupta    
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Some Thoughts computer exploration | Comment 1 of 5

   10    for Tot=2 to 2400
   20     for X=1 to Tot-1
   30       Y=Tot-X
   40       Lhs=5^X+12^Y
   50       Z=log(Lhs)/log(13)
   60       Zr=int(Z+0.5)
   70       if Lhs=13^Zr then print X;Y;Zr,Lhs;13^Zr
   80     next X
   90    next Tot

finds only

 2  2  2         169  169

so that means there is no solution with x and y totalling under 2400, other than 2,2,2.

  Posted by Charlie on 2012-05-26 13:49:24
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