Question

1of3. Prove that any positive add integer
is of the form 4q+1 or 4q+ 3
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integes
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Answer 1

Answer:

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Answer 2

Questions should be:

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

ANSWER:

• Any positive odd integer is in the form of 4q+1 or 4q+3.

GIVEN:

• A positive integer which is Divided by 4.

TO PROVE:

• Any odd integer is in the form of 4q+1 or 4q+3.

SOLUTION:

Let n be any positive integer which is Divided by 4 we get some quotient'q' and remainder 'r'.

=> n = 4q+r. ...(i)

where r = 0,1,2,3

Putting r = 0 in eq(i)

=> n = 4q (Divisible by 2)

It is not an odd number.

Putting r = 1 in eq(i)

=> n = 4q+1 (Not Divisible by 2)

It is an odd number.

Putting r = 2 in eq(i)

=> n = 4q+2

=> n = 2(2q+1) [Divisible by 2]

It is not an odd number.

Putting r = 3

=> n = 4q+3 (Not Divisible by 2)

It is an odd number.

So any positive odd integer is in the form of 4q+1 or 4q+3.