Question: Let X = {0, 2, 4, 6, ...,200} (i.e., X contains all multiples of 2 between 0 and 200 inclusive) and suppose AC X

Let X = {0, 2, 4, 6, ...,200} (i.e., X contains all

Let X = {0, 2, 4, 6, ...,200} (i.e., X contains all multiples of 2 between 0 and 200 inclusive) and suppose AC X with |A| 53. Show there must exist distinct a, b A satisfying the following two properties simultaneously: (i) a + b is divisible by 51, and (ii) a - b is divisible by 4.

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