Question

Use euclid division lemma to show that the square of any positive integer is either 0 or 1 when divided by ,4

Answer 1

Answer:

Step-by-step explanation:

let a be any positive integer and b = 3.

then a = 3q + r for some integer q ≥ 0

And r = 0, 1, 2 because 0 ≤ r < 3

Therefore, a = 3q or 3q + 1 or 3q + 2

Or,

a² =(3q)² or (3q+1)² or (3q+2)²

a² =(9q²) or 9q² + 6q +1 or 9q² +12q +4

a² = 3x(3q²) or 3(3q² +2q)+1 or 3(3q² +4q+1)+1

a²= 3k₁ or 3k₂ +1 or 3k₃ +1

Where k₁, k₂, and k₃ are some positive integers

Hence, it can be said that the square of any positive integer is either of the form 3m or 3m+ 1.

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