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Use Euclid’s division lemma to show that the cube of any positiveinteger is of the form 9m, 9m + 1 or 9m + 8.Solution:Let a be any positive integer and b = 3a = 3q + r, where q ≥ 0 and 0 ≤ r < 3∴a=3qor3q+1or3q+2Therefore, every number can be represented as these three forms.There are three cases.Case 1: When a = 3q,a3=(3q)3=27q3=9(3q3)=9m,Where m is an integer such that m=3q in this solution why can't we take 9 m instead they have taken 3q

Answer»

Let a and b be any POSITIVE INTEGER
such that
a=bq+r
b=3, r=0,1,2 0<=ra=3Q,3q+1,3q+2
a^3=(3q)3=27q^3=9(3q^3)=9m where 3q^3 is m
a^3=(3q+1)3=
a^3=(3q+2)3=


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