Question

Show that any positive odd is of the form 4q+1 or4q+3 and solv

Answer 1

suppose that a is a positive odd number
and b=4
then
a÷6
r=0,1,2,3
because b is greater than r and r is greater than 0 and equal to 0
possible value of a is
4q,4q+1,4q+2,4q+3
then,
we know that,
4q=2(2q)
4q+2=2(2q+1)
a is a positive odd number
and 4q and 4q+2 is even numbers
because they are divisible by 2
so,any positive odd is of the form of 4q+1 and 4q+3
hope it helps you
please mark as brainlist

Answer 2

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 .