Question

show that any positive odd integer is of the form 4q+1 or 41+3 whare q is some integer . I need full experience​

Answer 1

Answer:

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Answer 2

Answer:

let a be any positive odd integer. Then, by using euclid's division lemma a= bq + r

where, b= 4 and r = r is greater than or equal to 0 and smaller than equal to b (4).

a = 4q + 0

a = 4q + 1

a = 4q + 2

a = 4q + 3

Here, 4q; 4q+2 ; is completely divisible by 2. So they are positive even integer.

And 4q +1; 4q + 3 are not completely divisible by 2 so they are positive odd integers.