Consecutive Integers

Number Theory Level pending

Two sets \(\{a_n\}\) and \(\{b_n\}\) of 4 consecutive positive integers have exactly one integer in common. Let

  • \(A\) denote the sum of the integers in \(\{a_n\}\), which is the set with the greater numbers, and
  • \(B\) denote the sum of the integers in \(\{b_n\}\).

Find \(A-B\).

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