23. Prove that any integers a, 9 f (a?-3)
Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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How do I prove the quotient theorem and division by cases for this problem
Transcribed Image Text:23. Prove that amy integers a, 9 { (a?-3)
Proof (by contradicton) :
Suppose not
. That is suppose a € Z and 9 (a-3)
ə a°: 9q +3 by definition of diwisibility.
for some intergers
a= 3K +1
or a = 3k+2
et k by de finition of the quotient remainder
epon theorem.
Case I ;
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