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Question
For all n ∈ N, 3.52n+1 + 23n+1 is divisible by ______.
Options
19
17
23
25
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Solution
For all n ∈ N, 3.52n+1 + 23n+1 is divisible by 17.
Explanation:
Let P(n): 3.52n+1 + 23n+1
For P(1): `3.5^(2.1+1) + 2^(3.1+1)`
= 3.53 + 24
= 3(125) + 16
= 375 + 16
= 23 × 17
= 391
So it is divisible by 17.
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