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Help needed with a Mathematical proof.
Автор Wasif_Shahzad, история, 8 месяцев назад, По-английски

Hello. If there's someone who knows a better way of explaining the second paragraph of induction part of this problem's editorial then please do it. I'm having a hard time understanding it.

Problem 1604-C Di-Visible Confusion

Thanks in advance.

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8 месяцев назад, # |
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Auto comment: topic has been updated by Wasif_Shahzad (previous revision, new revision, compare).

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8 месяцев назад, # |
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They are basically checking if there exists a number in range [2,i+1] which doesn't divide a[i] and in case they all divide it then it must be divisible by there lcm which is going beyond the limit of a[i] i.e, 10^9. So it's not possible for a[i] to be divisible by all number in [2,i+1] if i>=22.

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    8 месяцев назад, # ^ |
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    why only for $$$ i <= 23 $$$? I can understand that other numbers will be multiples of these numbers but what about prime numbers which are lets say on prime indices.

    for example: say some number $$$ x $$$ is at $$$ i = 48 $$$

    This case is confusing me only.

    Edit: sorry if I couldn't convey my doubt clearly but it is related to prime numbers in the array

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      8 месяцев назад, # ^ |
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      Ok let's take an example of array a = [1,5,3,7,2,16,31] , in this array 31 is a prime number and is also present at index 7(1-based indexing) , so we can simply delete 31 as it is not divisible by (i+1) i.e, 8.

      If still not clear pls tell me briefly.

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