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Triplet hunt (Posted on 2021-07-27) Difficulty: 3 of 5
Find all triplets of positive integers (x, y, z) such that 2x+1=7y+2z.

No Solution Yet Submitted by Danish Ahmed Khan    
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Some Thoughts computer exploration | Comment 1 of 3
clc, clearvars
digits(60)
for t=0:64
   for x=0:64
      z=t-x;
      if z>=0
         y=round(log(vpa(2)^x+1-vpa(2)^z)/log(vpa(7)));
         if vpa(2)^x+1==vpa(7)^y+vpa(2)^z && y>0
            disp([x y z vpa(2)^x+1]) 
         end
      end
   end
end

explores up to x+z=64 and finds

  x  y  z  LHS and RHS
[ 3, 1, 1, 9.0]
[ 6, 2, 4, 65.0]

  Posted by Charlie on 2021-07-27 11:29:33
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