Show that any positive even integer can be written in the from 6q,6q + 2 or 6q + 4,where q is an integer.
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according to division lemma
a=bq+r
r<b
let take b=6
for r=0
a=6q
for r=1
a=6q+1
for r=2
a=6q+2
for r=3
a=6q+3
for r=4
a=6q+4
for r=5
a=6q+5
since, a=6q+1;6q+3;6q+5 is a positive odd integer
therefore,6q,6q+2,6q+4 is any positive even integer
a=bq+r
r<b
let take b=6
for r=0
a=6q
for r=1
a=6q+1
for r=2
a=6q+2
for r=3
a=6q+3
for r=4
a=6q+4
for r=5
a=6q+5
since, a=6q+1;6q+3;6q+5 is a positive odd integer
therefore,6q,6q+2,6q+4 is any positive even integer
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