show that every positive odd integer is of the form 2q+1 where q is integer
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assume q=o
2×0+1=1
assume q=1
2×1+1=3
and it goes on continuously
2×0+1=1
assume q=1
2×1+1=3
and it goes on continuously
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Hey
Here is your answer,
Let a be any positive integer and b=2. Then, by Euclid's division lemma there exist integers q and r such that
a = 2q + r , where 0 = r < 2
now, 0 = r <2
=> 0= r= 1
=> r=0 or, r=1 ( because r is an integer)
therefore a =2 q, then a is an even integer.
we know that an integer can either be even or odd. Therefore any odd integer is of the form 2q +1.
Hope it helps you!
Here is your answer,
Let a be any positive integer and b=2. Then, by Euclid's division lemma there exist integers q and r such that
a = 2q + r , where 0 = r < 2
now, 0 = r <2
=> 0= r= 1
=> r=0 or, r=1 ( because r is an integer)
therefore a =2 q, then a is an even integer.
we know that an integer can either be even or odd. Therefore any odd integer is of the form 2q +1.
Hope it helps you!
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