Q. 184.3( 16 Votes )

Show that every p

Answer :

Let a be any odd positive integer and b = 4.

By division lemma there exist integer q and r such that


a = 4 q + r, where 0 ≤ r ≤ 4


so a = 4q or, a = 4q + 1 or, a = 4q + 2 or, a = 4q + 3


4q + 1 4 is divisible by 2 but 1 is not divisible by 2,so it is an odd number


4q + 2 4 is divisible by 2 and 2 is also divisible by 2,so it is an even number


4q + 3 4 is divisible by 2 but 3 is not divisible by 2,so it is an odd number


4q + 4 4 is divisible by 2 and 4 is also divisible by 2,so it is an even number


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


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

Show that the squNCERT - Maths Exemplar

Show that the squNCERT - Maths Exemplar

Using Euclid’s diNCERT - Maths Exemplar

Show that one andRS Aggarwal - Mathematics

One dividing a poRS Aggarwal - Mathematics

Show that the squNCERT - Maths Exemplar

Write whether theNCERT - Maths Exemplar