show that any positive integer is in the form 3q or 3q 1 or 3q 2 for some integer q
Answers
Answered by
8
Hiii Friend,
Let n be an arbitrary positive integer.
On dividing n by 3 , let Q be the Quotient and r be the Remainder .
Then by Euclid's division lemma , we have
n = 3Q+r , where r = 0,1,2
When r = 0
N = 3Q
When r = 1
N = 3Q+1
When r = 2
N = 3Q+2
Therefore,
N = 3Q or (3Q+1) or (3Q+2) , for some integer Q.
Thus, any positive integer is in the form of 3Q , (3Q+1) or (3Q+2) for some integer Q.
HOPE IT WILL HELP YOU ..... :-)
Let n be an arbitrary positive integer.
On dividing n by 3 , let Q be the Quotient and r be the Remainder .
Then by Euclid's division lemma , we have
n = 3Q+r , where r = 0,1,2
When r = 0
N = 3Q
When r = 1
N = 3Q+1
When r = 2
N = 3Q+2
Therefore,
N = 3Q or (3Q+1) or (3Q+2) , for some integer Q.
Thus, any positive integer is in the form of 3Q , (3Q+1) or (3Q+2) for some integer Q.
HOPE IT WILL HELP YOU ..... :-)
Answered by
0
To Show :
Any positive integer is of the form 3q or 3q+1 or 3q+2 .
Solution :
Let a be any positive integer .
Then b = 3
So by Euclid's Division lemma there exist integers q and r such that ,
a = bq+r
a = 3q+r (b = 3)
And now ,
As we know that according to Euclid's Division Lemma :
0 ≤ r < b
Here ,
0 ≤ r < 3
Here the possible values of r are = 0,1,2
=> 0 ≤ r < 1<2
=> r = 0 or r = 1 or r = 2
And then
a = 3q+r
a = 3q+0 = 3q
a = 3q+1
a = 3q+2
#Hence Proved !!
Similar questions