The following expression yields an integer answer (very surprisingly it seems).
$${\left (515391\frac{33}{40} \right)}^4 - {\left (384140\frac{39}{40} \right)}^4 = 48783404650404592720562$$
I have tried many other pairs of 6-digit integers , but none of them result in an integer answer. For example: $${\left (515390\frac{33}{40} \right)}^4 - {\left (384141\frac{39}{40} \right)}^4 = 48782630297643606282783.184$$
$${\left (515389\frac{33}{40} \right)}^4 - {\left (384142\frac{39}{40} \right)}^4 = 48781855946299371591451.728$$
$${\left (515392\frac{33}{40} \right)}^4 - {\left (384139\frac{39}{40} \right)}^4 = 48784179004582352493575.376$$
I have tried over a hundred pairs of 6-digit integers , but none of them result in an integer answer. It seems that a special property or characteristic of the pair of integers 515391 and 384140 , makes the above expression an integer. But what special property or characteristic ? Can anyone see why the above expression is an integer ?