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Challenge A. Prove that, ∀n ∈ N, n5/5 + n3/3 + 7n/15 ∈ Z.
Challenge B. Prove that, ∀n ∈ N, 25 | (16n + 10n − 1).
Question 2. Let a0, a1, a2, … be a sequence defined as follows:
a0 = 6, a1 = 9, a2 = 12, and ai = ai−1 − ai−3 for each integer i ≥ 3.
Determine the term a4, and prove that 3 | ai for each integer i ≥ 0.
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