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Let x, y, z be positive integers such that \(2^{3x} + 2^{4y} = 2^{5z}\).  Find the smallest possible value of z.

 Dec 8, 2019
 #1
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a=1; b=1;c=1;d=2^3*a + 2^4*b; if(d==2^5*c, goto5, goto6);printd,a,b,c; a++;if(a<100, goto3, 0);a=1;b++;if(b<100, goto3, discard=0; a=1;b=2;c++;if(c<100, goto3, 0)

 

The smallest values for x, y, z are:

 

x =2, y = 1 and z = 1

 Dec 8, 2019
 #2
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Wait a minute !! I fouled the numbers up:

 

The smallest x, y, z are: 

 

x = 8,  y = 6,  z = 5

 Dec 8, 2019

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