Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
1.7k views
in Number System by (50.2k points)
closed by

Show that any positive odd integer is of the form 4q + 1 or 4q + 3, where q is some integer.

1 Answer

+1 vote
by (55.4k points)
selected by
 
Best answer

Let a be any positive odd integer. We apply the division algorithm with a and b = 4.

Since 0 ≤ r < 4, the possible remainders are 0,1,2 and 3.

i.e. a can be 4q, or 4q + 1, or 4q + 2, or 4q + 3, where q is the quotient.

As we know a is odd, a can’t be 4q or 4q + 2 because they both are divisible by 2.

Therefore, any positive odd integer is of the form 4q + 1 or 4q + 3.

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...