Question

Show that any positive odd integer is often form 6q+1,6q+4 form odd integer

Answer 1

Hi!!!!!!

Here is the answer-----------------

let a be any positive integer and b=6 (a=bq+r)


Since 0<r<6 the possible remainders are 0,1,2,3,4,5

That is, a can be 6q or 6q+1 or 6q+4,where q is a quotient.

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Answer 2

Hi
According to EDL a=bq+r
Let us take b=6 so r=0,1,2,3,4,5
If r=0
a=6q+0 (divisible by 2 -even)
If r=1
a=6q+1 (not divisible by2-odd)
If r=2
a=6q+2 (divisible by2-even)
If r=3
a=6q+3 (not divisible by 2-odd)
If r=4
a=6q+4 (divisible by2-even)
If r=5
a=6q+5 (not divisible by 2-odd)

As the above suggest hence we came up to the conclusion that
every odd positive integer is of the form 6q+1,6q+3,6q+5

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