Question
Disprove the statement:
by providing a suitable counter-example.
Answer :
Word Count : 162
To disprove the statement: \[ (x + y)^n = x^n + y^n, \forall n \in \mathbb{N}, x, y \in \mathbb{Z} \] we need to find values of \( x \), \( y \), and \( n \) such that: \[ ________ _____ _____ ___ ____ __________ ________ ____ _________ _____ __________ __________.
_______ _________ _________ _______ ________ ____ _________ ______ ______ __________ _____ _____.
_________ ____ __________ __________ _______.
_______ ________ __________ _____ _________ _________ ____ ____ __________ _________ _______ ____.
_______ ________ _____ ____ _________ _________ _________.
_________ _________ ___ ______ ___ __________ ____ _____ ____ ___ ______ _____.
______ ___ ____ ______ _________.
__________ _____ ___ ____ ______ ___ _____ ________ _____.
____ _______ ________ ______ ____ ______ ________ __________ ___ ______ _____.
__________ ________ __________ __________ ________ ______ ______ ___ _______ _________.
______ ______ _____ _______ ______ ______ ______.
_____ __________ _______ _____ _________ ________ ______ ____.
_______ _________ _____ ___ ________ __________ __________ ______ ________ _______ ________.
_____.
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To disprove the statement: \[ (x + y)^n = x^n + y^n, \forall n \in \mathbb{N}, x, y \in \mathbb{Z} \] we need to find values of \( x \), \( y \), and \( n \) such that: \[ ________ _____ _____ ___ ____ __________ ________ ____ _________ _____ __________ __________.
_______ _________ _________ _______ ________ ____ _________ ______ ______ __________ _____ _____.
_________ ____ __________ __________ _______.
_______ ________ __________ _____ _________ _________ ____ ____ __________ _________ _______ ____.
_______ ________ _____ ____ _________ _________ _________.
_________ _________ ___ ______ ___ __________ ____ _____ ____ ___ ______ _____.
______ ___ ____ ______ _________.
__________ _____ ___ ____ ______ ___ _____ ________ _____.
____ _______ ________ ______ ____ ______ ________ __________ ___ ______ _____.
__________ ________ __________ __________ ________ ______ ______ ___ _______ _________.
______ ______ _____ _______ ______ ______ ______.
_____ __________ _______ _____ _________ ________ ______ ____.
_______ _________ _____ ___ ________ __________ __________ ______ ________ _______ ________.
_____.
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