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LET (36m+n)=2^x AND (m+36n)=2^y THEN,
(36m+n)(m+36n)=2^(x+y)
AlSO, x and y must me both integers

Now,
n=2^x - 36m
THEN,
m+36n=2^y
m+36(2^x-36m)=2^y
36 * 2^x -1295m=2^y

Now, I think I have to prove that y is never a integer

36-1295m/2^x= 4, 8, 16, 32
1295m/2^x=32, 28 ,16 ,4
2^x=1295m/32 , 1295m/28 , 1295m/16 , 1295m/4

Hence, (36 m+ n)(m+36 n) cannot be a power of 2.

I have jumped some step......... I hope I made it clear

looks like gcd is very important ... i never liked it.

Short and Neat :)