Question

Show that any positive odd integer is of the form 4q+1 or 4q+3,where q is some integer.......explain briefly bcoz it is 3mark question.....pls guys....

Answer 1

let,

a= be any positive integer
b = 4
by Euclid's division lemma,
a= bq + r
a = 4q + r

now a= 4q......... ( where r=0).
a= 4q +1......(where r =1)
a=4q+2........(where r=2)
a=4q+3.........(where r=3)

we know 1 and 3 are odd integers,
hence 4q+1 and 4q+3 are odd positive integers.

hope it helps

Answer 2

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.