Class 10 Maths · Real Numbers · NCERT Exercise 1.4 · Question 1

Real Numbers Hard

Show that the cube of a positive integer of the form 6q + r, q is an integer and r = 0, 1, 2, 3, 4, 5 is also of the form 6m + r.

Answer

Proved:

(6 q + r)^{3} = 6 m + r

, since every term of the expansion except

r^{3}

is divisible by 6, and

r^{3}

itself leaves remainder

r

modulo 6 for each

r = 0, 1, 2, 3, 4, 5

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