Ex 1.1, 4 - Use Euclid’s division lemma to show that square - Euclid's Division Algorithm - Proving

The rest of the post is locked. Join Teachoo Black to see the full post.


Ex 1.1 , 4 Use Euclid’s division lemma to show that the square of any positive integer is either of the form 3m or 3m+ 1 for some integer m. [Hint : Let x be any positive integer then it is of the form 3q, 3q+ 1 or 3q+ 2. Now square each of these and show that they can be rewritten in the form 3m or 3m+ 1.] As per Euclid’s Division Lemma If a and b are 2 positive integers, then a = bq + r where 0 ≤ r < b Let positive integer be a And b = 3 Hence a = 3q + r where ( 0 ≤ r < 3) r is an integer greater than or equal to 0 and less than 3 hence r can be either 0 , 1 or 2 Hence, square of any positive number can be expressed of the form 3m or 3m + 1 Hence proved

Go Ad-free
Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.