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Let x be any positive integer and y = 3.
By Euclid’s division algorithm, then,
x = 3q+r, where q≥0 and r = 0, 1, 2, as r ≥ 0 and r < 3.
Therefore, putting the value of r, we get,
x = 3q
or
x = 3q + 1
or
x = 3q + 2
Now, by taking the cube of all the three above expressions, we get,
Case (i): When r = 0, then,
x2= (3q)3 = 27q3= 9(3q3)= 9m; where m = 3q3
Case (ii): When r = 1, then,
x3 = (3q+1)3 = (3q)3 +13+3×3q×1(3q+1) = 27q3+1+27q2+9q
Taking 9 as common factor, we get,
x3 = 9(3q3+3q2+q)+1
Putting = m, we get,
Putting (3q3+3q2+q) = m, we get ,
x3 = 9m+1
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I think you have written the question wrong!!
Bcoz after question mark, why have u given the symbol of square????
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