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11 June, 16:38

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) ²

3) s+t

A) None

B) 1 only

C) 2 only

D) 3 only

E) 1 and 2

+3
Answers (1)
  1. 11 June, 18:35
    0
    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)
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