First of all, we can consider a 5 = b 4, which shows that a must be a number of the fourth power and b is a number of the fifth power.

c？ =d？ C is a quadratic number, d is a cubic number,

Let a = m 4, b = m 5 and c=n? ，d=n？ ,

A-c= 17, that is, (m? +n)(m？ -n)= 17，

∫ 17 is a prime number. m？ +n，m？ -n is a natural number, m? +n>m？ -n，

∴m？ +n= 17，m？ -n= 1，

∴m=3,n=8，

Through observation, we can get: a=8 1, c=64,

∴d-b=n？ -m^5=8？ -3^5=5 12-243=269.