Math, asked by sakthi3399, 1 year ago

Show that any odd positive integer is of the form 4q+1 or 4q+3 where q is some integer.

Answers

Answered by pradeepchoudhary1531
1

see example no. 3 in ncert book chapter 1

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sakthi3399: Tq. But I don't need this method
pradeepchoudhary1531: ok
pradeepchoudhary1531: I send you some other method
Answered by Anonymous
2

Step-by-step explanation:

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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