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Show the every positive odd integer …

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Show the every positive odd integer is the form 4m+1 and 4m+3 where m is form of some integers

Posted by Sukhdev Nirankari 6 years, 7 months ago

CBSE > Class 10 > Mathematics

1 answers

Gaurav Seth 6 years, 7 months ago

Step-by-step explanation:

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

1Thank You

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CBSE > Class 10 > Mathematics