Question

Use Division Algorithm to show that any Positive Integer is the form 6q (or) 6q+3 (or) 6q+5, where 'q' is One Integer.
Chapter: Real Numbers
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Answer 1

Step-by-step explanation:

Let: ‘a’ be any positive integer

⇒ Euclid’s Algorithm: a = bq + r [0 < r < b]

                                    a = 3q + r [0 < r < 3]

∴ b = 3, r = 0,1,2

∴ If r = 0, put the values of 'r' in Eq --- (1)

a = bq + r

a = 3q + 0

a = 3q

∴ If r = 1, put the values of 'r' in Eq --- (1)

a = bq + r

a = 3q + 1

∴ If r = 2, put the values of 'r' in Eq --- (1)

a = bq + r

a = 3q + 2

= (a)² = (3p)²

= (a)² = (3p + 1)²

= (a)² = 3 (3p + 6p + 1)²

= (a)² = 6p + 1