Math, asked by abdul9441927024, 1 year ago

Show that any positive odd integer is of the form 4q+1 and 4q+3 where q is a positive integer

Answers

Answered by A1111
20
Hope this helps.....
Attachments:
Answered by Anonymous
19

Step-by-step explanation:


Let a be the positive integer.


And, b = 4 .


Then by Euclid's division lemma,


We can write a = 4q + r ,for some integer q and 0 ≤ r < 4 .


°•° Then, possible values of r is 0, 1, 2, 3 .


Taking r = 0 .


a = 4q .



Taking r = 1 .


a = 4q + 1 .


Taking r = 2


a = 4q + 2 .


Taking r = 3 .


a = 4q + 3 .


But a is an odd positive integer, so a can't be 4q , or 4q + 2 [ As these are even ] .



•°• a can be of the form 4q + 1 or 4q + 3 for some integer q .



Hence , it is solved



THANKS



#BeBrainly.


Similar questions