Question

use division algorithms to show that the square of any positive integer is of the from 3p or 3p+1.​

Answer 1

Answer:

Given : square of any integer is of the form 3p or 3p+1.

To find : Prove.

Solution: Any number can be represented as. 3q , 3q + 1 , 3q + 2 where q is integer. (3q)² = 9q² = 3* 3q² = 3p ( as q is integer => 3q² is integer) (3q + 1)² = 9q² + 6q + 1. = 3( 3q² + 2q) + 1. 3q² + 2q is an integer as q is integer. = 3p + 1. (3q + 2)²

Answer 2

• Given : square of any integer is of the form 3p or 3p+1.
• To find : Prove.
• Solution: Any number can be represented as. 3q , 3q + 1 , 3q + 2 where q is integer. (3q)² = 9q² = 3* 3q² = 3p ( as q is integer => 3q² is integer) (3q + 1)² = 9q² + 6q + 1. = 3( 3q² + 2q) + 1. 3q² + 2q is an integer as q is integer. = 3p + 1. (3q + 2)²

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