show that every positive even integer is of the form 2q and that every positive integer i of the form 2q+1,where q is some integer.

Asked by FEHMEEDAH NAZNEEN | 7th Jul, 2010, 12:00: AM

Expert Answer:

Dear student, following is the answer to your query:

Let a be any positive integer and b = 2.

Applying Euclid’s algorithm, we have:

a = 2q + r, for some integer q ≥ 0, and 0 ≤ r < 2

a = 2q or 2q + 1

If a = 2q, then a is an even integer.

Now, a positive integer can either be even or odd. Thus, any positive odd integer is of the form 2q + 1.



Answered by  | 14th Jul, 2010, 02:45: PM

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