Question

Show that any positive odd integer is of the form 6q+1, or 69 + 3, or 6q+ 5, where q is
some integer​

Answer 1

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Let a be the positive odd integer which when divided by 6 gives q as quotient and r as remainder. but here, a=6q+1 & a=6q+3 & a=6q+5 are odd.

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Answer 2

Answer:

Let

′

a

′

be any positive integer and b=6

Then by division algorithm

a=6q+r where r=0,1,2,3,4,5

so, a is of the form 6q or 6q+1 or 6q+2 or 6q+3 or

6q+3 or 6q+4 or 6q+5

Therefore If s is an odd integer

Then

′

a

′

is of the form 6q+1 or 6q+3 6q+5

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