AMC 10 Daily Practice Round 1

Complete problem set with solutions and individual problem pages

Problem 10 Medium

How many integer values of n satisfy the equation of {{\left( {{n}^{2}}-n-1 \right)}^{n+2}}=1?

  • A.

    0

  • B.

    1

  • C.

    2

  • D.

    3

  • E.

    4

Answer:E

n+2=0, {{n}^{2}}-n-1\ne 0, n=-2,

{{n}^{2}}-n-1=1, n=-1, n=2;

{{n}^{2}}-n-1=-1 and n+2 is even, n=0.

Thus, n=-1, -2, 0, 2. There are \boxed{E: 4} integer values of n.

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