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Standard X
Mathematics
Method of Finding HCF
If 'n' is any...
Question
If 'n' is any positive integer then by Euclid algorithm. Show that n can be expressed in the form of 3m or 3m+1 ; where 'm' is some integer.
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Q.
If
n
be any positive integer, then by using Euclid's division algorithm, show that
(i)
n
3
can be expressed in the form
9
m
,
9
m
+
1
or
9
m
+
8
.
(ii)
n
3
+
1
can be expressed in the form
9
m
,
9
m
+
1
or
9
m
+
2
.
Here,
m
is some integer.
Q.
Let Euclids division lemma to show that the square of any positive integer is either of the form
3
m
or
3
m
+
1
for some integer
m
.[Hin: Let
x
be any positive integer then it is of the form
3
q
,
3
q
+
1
or
3
q
+
2
. Now square each of these and show that they can be rewritten in the form
3
m
or
3
m
+
1
Q.
Show that the square of any positive integer is of the form
3
m
or,
3
m
+
1
for some integer
m
.
Q.
Question 4
Use Euclid's division lemma to show that the square of any positive integer is either of the form 3m or 3m + 1 for some integer m.
[Hint: Let x be any positive integer then it is of the form 3q, 3q + 1 or 3q + 2. Now square each of these and show that they can be rewritten in the form 3m or 3m + 1.]
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