a = 5^10 - 625^2 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?
Choices.
A) None  B) One  C) Two  D) Three  E) Four
This is a tricky worded question and I think the answer is should be D not C...   Here is my reason :   The stem says that x is a positive integer such that has no factor grater than 2 and less than x itself . The stem wants to say that X is a PRIME NUMBER . because any prime   Number has no factor grater than 1 and Itself .   On the other hand the stem says that X COULD get how many different number NOT MUST get different number ( this is very important issue )   AS our friends say, if we simplify Numerator more we can obtain : 5^12 ( 5^3-1) = 5^12 (124) = 5^12 (31*2*2) divided by x and we are told that this fraction is   An integer . so, X TwoOULD Be ( not Must be) 5 , 31 ,or 2 !!! so , X could get 2 different values and answer is Two....
<result>C</result>
a = 5^10 - 625^2 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?