Question

prove that every odd positive integer can be expressed in from 4q+1 and 4q+3 where q is an integer

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Answer 1

Step-by-step explanation:

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ANSWER

We have

Any positive integer is of the form 4q+1or4q+3.

As per Euclid’s Division lemma.If a and b are two positive integers,

then,a=bq+r

Where 0≤r<b.

Let positive integers be a.and b=4

Hence,a=bq+r

Where, (0≤r<4)R is an integer greater than or equal to 0 and less than 4.

Hence, r can be either 0,1,2and3

Now, If r=1

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