1s and 0s

Which is the smallest prime p p such that none of the numbers 11...10...00 11...10...00 (starting with an integer number of 1’s followed by an integer, equal or different, number of 0’s) is multiple of p p ? Type 0 if you think there’s none such prime number


The answer is 0.

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1 solution

Emanuele Prati
Apr 17, 2019

Let’s take p + 1 p+1 numbers made of 1s (1, 11, 111, ...) and their remainder modulo p p . For the Pigeonhole Principle, there are at least two of this numbers with the same remainder, so their difference will be a number made by 1s followed by 0s and multiple of p p whatever is p p .

Very nice!

Chris Lewis - 2 years, 1 month ago

I didn't get the question

Uttam Manher - 2 years, 1 month ago

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