show that one and only one out of a,a+2,a+4 is divisible by 3, where a is any integer
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case 1 - let a is divisible by 3
so a+2 cannot be divisible by 3 as 2 is not a multiple of 3 .
similarly a+4 is not divisible by 3 .
case 2- let a+2 is divisible by 3
so a is not divisible by 3 as 2 is not a multiple of 3 and subtracting a number other than its multiple from its dividient cannot be a it's multiple.
similarly we can prove for a+4 .
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Answer:see answer in the attachment below
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