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

  

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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. 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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8 X 20 246 AC A 53 A 54 56 582... View the full answer