Question

Euclid
division Lemma to show
any positive integer is
of
that the
of the form
9m
9m+1
9m+8​

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

Answer:

MATHS

Use Euclid's division lemma to show that cube of any positive integer is either of the form 9m, 9m + 1 or 9m + 8 for some integer 'm'. 

December 26, 2019Ateeba Hussaini

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ANSWER

Let a and b be two positive integers, and a>b

a=(b×q)+r where q and r are positive integers and 

0≤r<b

Let b=3 (If 9 is multiplied by 3 a perfect cube number is obtained) 

a=3q+r where 0≤r<3

(i) if r=0,a=3q    (ii) if r=1,a=3q+1      (iii) if r=2,a=3q+2

Consider, cubes of these

Case (i) a=3q

a3=(3q)3=27q3=9(3q3)=9m           where m=3q3 and   'm' is an integer.

Case (ii) a=3q+1

a3=(3q+1)3                [(a+b)3=a3+b3+3a2b+3ab2]

      =27q3+1+27q2+9q=27q3+

HOPE IT HELPS!!!