show that any positive odd integer is of the form 4 Q + 1 or 4Q+ 3 where Q is some integer
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Let any positive integer a = 4q + r
0<_r<_4
r=0,1,2,3
a=4q+0
a=4q+1
a=4q+2
a=4q+3
Required odd integer are=4q+1,4q+3
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Aksharawat:
is this correct
Answered by
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Step-by-step explanation:
Note :- 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 a = 4q + r ,for some integer q and 0 ≤ r < 4 .
°•° Then, possible values of r is 0, 1, 2, 3 .
Taking r = 0 .
a = 4q .
Taking r = 1 .
a = 4q + 1 .
Taking r = 2
a = 4q + 2 .
Taking r = 3 .
a = 4q + 3 .
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 .
Hence , it is solved
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