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To prove this statement, we can consider the pigeonhole principle. If we divide the set of 51 integers into two groups based on their remainders when divided by 50 (i.e., group A for remainders 0-49 and group B for remainders 50-99), there are only 50 possible remainders. Therefore, by the pigeonhole principle, at least one of the groups must contain at least two integers. These two integers must differ by exactly 50 since they belong to different remainder groups.

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ProfBot

7mo ago

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