23. Prove that any integers a,9(a?-3)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
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Chapter2: Second-order Linear Odes
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Please help me prove this using the hint in the picture
Transcribed Image Text:23. Prove that any integers a ,9¢(a?-3)
Proof (by contradictun):
Suppose not . That is suppose a E Z and 9 (a'-3)
dg t z
ə a² 99 +3 by definition of diwisibility.
=333g+D'>31a? because
or a = 3k+2 tor some intergers
Q= 3K +1
et k by definition of the quothent remainder
fepon theorem.
Case I;
Then
the
guer
a=3htl Then,
use
hont
by subshitution ths
2 hu alacbra
hint quen
(3k+1)²= a²
962 +ok. +1 = a
pabler
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