1s and 0s
Which is the smallest prime such that none of the numbers (starting with an integer number of 1’s followed by an integer, equal or different, number of 0’s) is multiple of ? Type 0 if you think there’s none such prime number
The answer is 0.
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1 solution
Let’s take p + 1 numbers made of 1s (1, 11, 111, ...) and their remainder modulo 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 whatever is p .