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Problem Solving (PS) | Re: a = 5^15 - 625^3 and a/x is an integer, where x is a positive integer

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nikitathegreat wrote:

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?

A. None
B. One
C. Two
D. Three
E. Four

Can someone help explain how do we know that x is a prime no. ?

It says that x doesnt have a factor p. If I take x =6, then we can have 1<5<6. here 5 is not a factor of 6 and 6=x is not a prime no.? I am not able to interpret the statement that x is prime no.

Thanks


6 does have factors p such that 1 < p < 6. For example, both 2 and 3 are factors of 6, satisfying 1 < p < 6. Only prime numbers satisfy the statement because a prime number has exactly two factors: 1 and itself, and does not have any other factor p such that 1 < p < prime.

Statistics : Posted by Bunuel • on 15 May 2015, 03:50 • Replies 7 • Views 10853



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