Question

show that any positive even integer can be written in the form 6q 6q + 2 or 6q + 4 where Q is an integer ​

Answer 1

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Answer 2

Answer:

Let a be any positive even integer.

let b = 6( divisor )

Therefore by Euclid's Division Algorithm

a = 6q + r where 0<=r<b

but a is even

therefore r = 0,2,4

Case 1 r = 0

a = 6q

Case 2 r = 2

a = 6q + 2

Case 3 r = 4

a = 6q + 4

Form the above Cases

We can say

Hence Proved

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