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Prove that if m and n are positive integers and x is a
Chapter 2, Problem 26E(choose chapter or problem)
Prove that if \(m\) and \(n\) are positive integers and \(x\) is a real number, then
\(\left\lfloor\frac{\lfloor x\rfloor+n}{m}\right\rfloor=\left\lfloor\frac{x+n}{m}\right\rfloor\)
Equation Transcription:
Text Transcription:
m
n
x
[[x]+n/m]=[x+n/m]
Questions & Answers
QUESTION:
Prove that if \(m\) and \(n\) are positive integers and \(x\) is a real number, then
\(\left\lfloor\frac{\lfloor x\rfloor+n}{m}\right\rfloor=\left\lfloor\frac{x+n}{m}\right\rfloor\)
Equation Transcription:
Text Transcription:
m
n
x
[[x]+n/m]=[x+n/m]
ANSWER:
Solution:
Step1
Given that
We have to prove that if m and n are positive integers and x is a real number, then
Step2
We have m and n are positive integers and x is a real number.
Suppose x= b+y where b is an integer and
Then we have
L.H.S(left hand side)