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Triplet hunt (Posted on 2021-07-27)

Find all triplets of positive integers (x, y, z) such that 2^x+1=7^y+2^z.

No Solution Yet Submitted by Danish Ahmed Khan

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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

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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