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  3. 1. prove that given n + 1 natural numbers, there a

1. Prove that given n + 1 natural numbers, there are always two of them such...

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Advance Math

1. Prove that given n + 1 natural numbers, there are always twoof them such that their difference is a multiple of n.

2. Prove that there is a natural number composed with the digits0 and 5 and divisible by 2018.

both questions can be solved using pigeonhole principle.

Answer & Explanation Solved by verified expert
3.8 Ratings (472 Votes)
1 Here since there are only n possible remainders on division by n and we have n 1 numbers by the Pigeonhole Principle PHP some two of them have the same remainder on division by n Thus we can write these two as n1 nk1 r and n2 nk2 r where r is    See Answer
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