Question

Write whether every positive integer can be of the form 4q + 2, where q is an integer. Justify your answer

Answer 1

Answer:

4q+2 is even

Step-by-step explanation:

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Answer 2

Given,

4q + 2, where q is an integer.

To Find,

Every positive integer can be of the form 4q + 2

Solution,

Let a be a given positive number.

On dividing a by 4, let q be the quotient and r be the remainder.

Then, by Euclid's algorithm,we have:

a = 4q + r where 0 ≤ r < 4

a = 4q + r where r = 0,1,2,3

a = 4q + 2 = 2(2q+1)

It is clearly shown that 2q+1 is divisible by 2.

Therefore,4q+2 is a positive integer.

Hence, every positive integer can be of the form 4q + 2.