Page 102 - Numbertheory

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. 2k +1, 2k + 3, 2k + 5, 2k + 7, 2k + 9

(2k +1) + (2k + 3) + (2k + 5) + (2k + 7) + (2k + 9) = 105
10k + 25 = 105
10k = 80
k =8

. 2k + 9 = 16 + 9 = 25

2n n ≥ 1 ()
.

2n = 2 × 2n−1 = 2n−1 + 2n−1 = (2n−1 −1) + (2n−1 +1)

. 2n−1 + 1 2n−1 −1

()

. 2k + 3 2k +1

2k + 3 = 3(2k +1)
2k + 3 = 6k + 3

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