If x and y are positive integers such that (x-4) (x-10)=2^y , find the maximum possible value of x+y .

Step-by-step solution

aligned & Let y=a+b & (x-4)(x-10)=2^a 2^b & x=2^a+4 or 2^b+10 (vice-versa). & x=2^a+4=2^b+10 . aligned aligned & 2^a-2^b=6 . & a=3 and b=1 . y=4 and x=12 & x+y=16 . aligned