Answer:
Step-by-step explanation:
I am taking q as some integer.
Let a be the positive integer.
And, b = 4 .
Then by Euclid's division lemma,
We can write [tex]a = 4q + r[/tex] ,for some integer [tex]q\ \text {and}\ 0 \leq r < 4 .[/tex]
°•° Then, possible values of r is 0, 1, 2, 3 .
[tex]\texttt {Taking} \ r = 0 .\\\\a = 4q .[/tex]
[tex]\texttt {Taking} \ r = 1 .\\\\a = 4q + 1 .\\\\\texttt {Taking} \ r = 2\\\\a = 4q + 2 .\\\\\texttt {Taking} \ r = 3 .\\\\a = 4q + 3 .[/tex]
But a is an odd positive integer, so a can't be 4q , or 4q + 2
[ As these are even ] .
•°• a can be of the form 4q + 1 or 4q + 3 for some integer q .
