Show that the square of any positive integers is either of the form 3m or 3m + 1 for some ineteger m. Question Show that the square of any positive integers is either of the form 3m or 3m + 1 for some ineteger m. in progress 0 Math Samantha 2 weeks 2021-09-04T17:34:13+00:00 2021-09-04T17:34:13+00:00 2 Answers 0 views 0

## Answers ( )

Answer:Use Euclid division lemma to show that the square of any positive integer is either of the form 3m or 3m+1 for some integer m. Let a be any positive integer and b = 3. =) … =) a = 3q or 3q + 1 or 3q + 2 for positive integer q.

## Question :–

Show that the square of any positive integers is either of the form 3m or 3m + 1 for some ineteger m.

## Solution :–

Let the required integer be,

## ATQ,

Squaring both sides,

⓵ If r = 0

Where m = is another integers.

⓶ If r = 1

Where m = is another integers.

⓷ If r = 2

Where m = is another integers.