If a,b,k, and m are positive integers, is a to the kth power a factor of b to the mth power?
(1) a is a factor of b.
(2) k<=m.
(1) a is a factor of b.
(2) k<=m.
Question is: Is a^k a factor of b^m?Mjkourtis wrote:If a,b,k, and m are positive integers, is a to the kth power a factor of b to the mth power?
(1) a is a factor of b.
(2) k<=m.
Or Is a^k * N = b^m for any integer N, which implies N = b^m/a^k
So, the question is asking if N is an integer greater than 0?
(1) a is a factor of b implies a * P = b implies N = (a^m)(P^m)/(a^k) implies N = a^(m - k) * (y^m)
If m < k, and a is not a factor of P, then N will not be an integer.
Example: If a = 2, b = 6, then 2 is a factor of 6
2² = 4 is a factor of 6² = 36
2^3 = 8 is NOT a factor of 36; NOT sufficient.
(2) k ≤ m is clearly NOT sufficient, as does not tell anything about a, b.
Combining (1) and (2), N = a^(m - k) * P^m and k < m
Hence N is an integer; SUFFICIENT.
The correct answer is C.
