A community for students. Sign up today!
Here's the question you clicked on:
← 55 members online
 0 viewing
 2 years ago
prove that the square of any integer a is either of the form 3k or 3k+1 for some integer k. [hint by division algorithm, a must be of the form 2q, 3q +1, or 3q+2]
 2 years ago
prove that the square of any integer a is either of the form 3k or 3k+1 for some integer k. [hint by division algorithm, a must be of the form 2q, 3q +1, or 3q+2]

This Question is Closed

matricked
 2 years ago
Best ResponseYou've already chosen the best response.1any integer can be written as 3q, 3q +1, or 3q+2....q being an integer case 1 when n=3q clearly n^2=9q^2=3(3q^2)

matricked
 2 years ago
Best ResponseYou've already chosen the best response.1when n=3q +1 n^2=9q^2+6q+1=3(3q^2+2q)+1

matricked
 2 years ago
Best ResponseYou've already chosen the best response.1when n=3q +2 n^2=9q^2+12q+4=3(3q^2+4q+1)+1 (form 3k+1)

matricked
 2 years ago
Best ResponseYou've already chosen the best response.1the square of any integer a is either of the form 3k or 3k+1
Ask your own question
Ask a QuestionFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.