Question

Example 3. Use Euclid's division lemma to show that the square of any positive
eger is either of the form 3 m or 3 m +1 for some integer m.
Solution : Let a be any positive integer.
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Answer 1

Answer:

let a be the square of an integer

therefore m=3

(Euclid division of lemma a=bq+r) (0< are equal to r<b)

since 0<are equal to r<3 (0,1,and3)

a=bq+r

A=3m or 3m+1 or 3m+2

therefore

the square of any positive integer is in the form of 3m, 3m+1, 3m+2