a = 5^15 - 625^3 and a/x is an integer, where x is a positive integer greater than 1, such that it does NOT have a factor p such that 1 < p < x, then how many different values for x are possible?
Choose the correct choice:  A) None  B) One  C) Two  D) Three  E) Four
a= 5^15 - 625^3 =&gt; 5^15 - (5^4)^3 =&gt; 5^15 - 5^12 = 5^12(5^3 - 1) = 5^12*124   124 = 31*4   a/x is integer   For condition of 2&lt;p&lt;x only 5 and 31 satisfies this   Hence answer is Two
<result>C</result>
a = 5^15 - 625^3 and a/x is an integer, where x is a positive integer greater than 1, such that it does NOT have a factor p such that 1 < p < x, then how many different values for x are possible?