Question

Show that positive even integers are in the form of 6m, 6m+2,6m+4 where in the form of integer

Answer 1

Answer:

Let a and b be any positive integers

a = bm + r, 0  r

Let b = 6. Then, r = 0,1,2,3,4,5

 a = 6m + r, where r = 0, 1, 2, 3, 4, 5

When r = 0, a = 6m even

When r = 1 a = 6m + 1 odd

When r = 2 a = 6m + 2 even

When r = 3 a - 6m + 3 odd

When r = 4 a = 6m + 4 even

When r = 5 a = 6m + 5 odd

Hence, all positive even integers are of the form 6m, 6m + 2 or 6m + 4.

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