Question

Show that every positive integer is either of the form 3m or 3m+1 or 3m+2 for some positive integer ‘m’

Answer 1

Step-by-step explanation:

Let A be any positive integer,

now, by Euclids Division Lemma,

"a=bq+r"

now, b=3

therefore, 'r' should be 0, 1 or 2 {B'coz 0<r}

now, when r = 0

then,

a=3q+r

a=3q+0

a=3q

========

when r = 1

a=3q+r

a=3q+1

========

when r = 2

a=3q+r

a=3q+2

HENCE PROVED

Answer 2

Step-by-step explanation:

Let A be any positive integer,

now, by Euclids Division Lemma,

"a=bq+r"

now, b=3

therefore, 'r' should be 0, 1 or 2 {B'coz 0<r}

now, when r = 0

then,

a=3q+r

a=3q+0

a=3q

========

when r = 1

a=3q+r

a=3q+1

========

when r = 2

a=3q+r

a=3q+2

HENCE PROVED