a must be greater than 4.

(4a + 1)/(a + 4) is an integer

Let x = a + 4. Then x must be greater than 8.

Then a = x - 4. Substituting,

(4x - 15)/x is an integer

So 15/x must be an integer.

So x must be 15.

a = x - 4 = 11

41 base 11 = 45, and 14 base 11 = 15, and 41/14 = 3