text: This number is the output when the Möbius function is applied to a prime number.
full_question: This number is the output when the Möbius function is applied to a prime number. The product of all four basis elements of the quaternions, one times i times j times k, equals this number. The Legendre symbol of a over p is this number if a is NOT a quadratic residue modulo p. Every bit in this number's two's complement representation is a 1. According to (*) Euler's identity, this number equals e to the power of i times pi. This is the only value achieved exactly once by cosine in the range 0 to 2pi, inclusive. Raising a number to this power is the same as finding its reciprocal. For 10 points, identify this additive inverse of one, which is equal to the square of the imaginary number i.
first_sentence: This number is the output when the Möbius function is applied to a prime number.
raw_answer: negative one 