Question

show that any positive even integer can be 6q+4 where q ia an integer​

Answer 1

Let a be any positive integer

on dividing a by 6 let q be the quotient and r be the remainder.

Now by Euclids division lemma,

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

when a=0 then a=6q

when a=1 then a=6q+1

when a=2 then a=6q+2

when a=3then a=6q+3

a=6q+4

a=6q+5

Clearly we can see that a is a positive even integer.

Therefore,Any positive integer can be 6q,6q+2,6q+3,6q+4.

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