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show that any positive odd integer is of the form (4m+1) or (4m+3) where m is some integer.

Posted by Aditya Bhashkar 6 years, 4 months ago

CBSE > Class 10 > Mathematics

1 answers

Yogita Ingle 6 years, 4 months ago

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

2Thank You

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