Multiple Choice Question (MCQ)

If a,b,c are positive integers such that a>b and a^2-ab-ac+bc = 7. then the value of a-c is

  1. ×

    -1

  2. ×

    -1 or -7

  3. ×

    1

  4. 1 or 7

Collected in the board: Number Theory

Steven Zheng posted 17 hours ago

Answer

  1. a^2-ab-ac+bc

    =a(a-b)-c(a-b)

    =(a-b)(a-c)=7

    Since 7 is a prime number, it has only 1 and itself as its factors.

    a > b implies a-c>0

    Therefore

    the value of a-c is 1 or 7

    D is the right choice

Steven Zheng posted 17 hours ago

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