If s and t are integers greater than 1 and each is a factor of the integer n, which of the following must be a factor of n^{st}?

1) s^t

2) (st) Â²

3) s+t

A) None

B) 1 only

C) 2 only

D) 3 only

E) 1 and 2

Question

Mathematics

Pamela Brandt

2 February, 03:43

If s and t are integers greater than 1 and each is a factor of the integer n, which of the following must be a factor of n^{st}?

1) s^t

2) (st) Â²

3) s+t

A) None

B) 1 only

C) 2 only

D) 3 only

E) 1 and 2

+1

Answers (1)

Know the Answer?

Kailyn Haynes · Answer 1

E) 1 and 2

Step-by-step explanation:

We are given that there are two integers (s and t) and they are factors of another integer (n). For example if s = 3 and t = 2, we can have n = 6.

Thus:

n^ (st) = 6^ (2*3) = 6^6 = (2^6) (3^6)

For the first condition: s^t = 3^2 is a factor of (2^6) (3^6)

For the second condition: (st) ^2 = (3*2) ^2 = 6^2 is a factor of 6^6

For the third condition: s+t = 3+2 = 5 is not a factor of 6^6 or (2^6) (3^6)

Therefore, only 1 and 2 are factors of n^ (st)

If s and t are integers greater than 1 and each is a factor of the integer n, which of the following must be a factor of n^{st}?1) s^t2) (st) Â²3) s+tA) NoneB) 1 onlyC) 2 onlyD) 3 onlyE) 1 and 2

If s and t are integers greater than 1 and each is a factor of the integer n, which of the following must be a factor of n^{st}?

1) s^t

2) (st) Â²

3) s+t

A) None

B) 1 only

C) 2 only

D) 3 only

E) 1 and 2