Take: $2^{20} = 2^{15}x+y$

Subtract $2^{15}x$ from both sides to get: $2^{20} - 2^{15}x=y$

Factor: $2^{15}(2^{5}- x)=y$

Rewrite as: $y=2^{15}(32- x)$

Since x and y are non-negative integers, we can conclude that $0<x≤32$ (i.e, if x > 32, y is negative)

Notice that, if $x=1$, $y=2^{15}(32- 1)=2^{15}(31)$, which is a little bit less than $2^{20}$
In other words, the maximum value of y is a little bit less than $2^{20}$

Also, if $x=32$, $y=2^{15}(32-32)=2^{15}(0)=0$

So, the minimum value of y is $0$ AND $x=32$ is the maximum value of x

As such, the minimum value $|x − y|$ is $|32 − 0|=32=2^5$

Answer: C

Cheers,
Brent