Math, asked by Aksharawat, 1 year ago

show that any positive odd integer is of the form 4 Q + 1 or 4Q+ 3 where Q is some integer

Answers

Answered by a0r1un200527
5

Let any positive integer a = 4q + r

0<_r<_4

r=0,1,2,3

a=4q+0

a=4q+1

a=4q+2

a=4q+3

Required odd integer are=4q+1,4q+3

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Aksharawat: is this correct
Answered by Anonymous
7

Step-by-step explanation:


Note :- I am taking q as some integer.



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.



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