Simply factoring:

5

^{20}- 5^{19}= 5^{19}(5 - 1) = 5^{19}(4), which is divisible by 2 (that is,**it is even**)Tinny F.

asked • 05/13/17Without using calculator kindly help proof the question, it involves prime power proof.

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Simply factoring:

5^{20} - 5^{19} = 5^{19}(5 - 1) = 5^{19}(4), which is divisible by 2 (that is, **it is even**)

Arturo O. answered • 05/13/17

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To prove it is even, it is sufficient to show it equals 2n, where n is any integer.

5^{20} - 5^{19} = 5^{19}(5^{1} - 5^{0}) = 5^{19}(5 - 1) = 5^{19}(4) = 2[2(5^{19})]

Let n = 2(5^{19})

Then

5^{20} - 5^{19} = 2n, i.e. a multiple of 2, so it is even

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