Question

Show that any positive odd integer is of the form 6q + 1 or 6 q + 3or 6q+ 5 where q is some integer?

Answer 1

Answer:

Let the positive integer be a and b=6

According to Euclid's division lemma,

a=bq+r where.. 0<and=r<b

Here, a=6q+r....0<and=r<6

So possible values of b are 0,1...5.

Now,

CASE1:r=0

a=6q+0

a=6q.....................EVEN

CASE2: r=1

a=6q+1................ODD

CASE3: r=2,

a=6q+2.................EVEN

CASE4: r=3................

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DO SIMILARLY REST Part...............

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Hence,any positive odd integer is of the form 6q+1,6q+3 or 6q+5

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