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Standard X
Mathematics
Euclid's Division Lemma
USE EUCLID DI...
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USE EUCLID DIVISON LEMMA TO SHOW THAT THE SQUAREOF ANY POSITIVE INTEGER IS EITHER OF THE FORM 3m or 3m+1or 3m+2 FOR SOME INTEGER m.
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Q.
Use 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
.
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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