Denote by R(N) the integer obtained by reversing the digits of a positive integer N.

Determine the largest integer that is certain to
divide N^{4} - (R(N))^{4}, with N > R(N), regardless of the choice of N.

**answer: 99.**

**x^4-y^4= (x^2-y^2)***** (****x^2+y^2) and**

** (x^2-y^2)= (x-y)***** (x+y)***** **

**If **

**x= 1000a+ 100b+****10c+d**

**and **

**y=****1000d+ 100c+****10b+a**

**x-y is divisible by 9**

**x+y ****is divisible by 11**

**ergo the product is divisible by 99 for any x and y if one is reverse of the other**

**x^2+y^2 contributes nothing**

**qed**