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Gokul43201

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What do you think? Care to try showing that numbers ending in 1,3,5,7, or 9 can not be even?

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Then n is even means 2 divides 10a+b, i.e. 2 divides b (let 10a+b=2k and solve for b). Hence b=0,2,4,6,8

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An explanation such as this is alright for proving that an integer [tex]n[/tex] is even if [tex]n=2k[/tex], for some integer [tex] k.[/tex] Thus, we have to use our knowledge of even numbers to say that they end in an integer that is divisible by 2. A satisfactory explanation, no doubt, just not what I'm looking for.

Then n is even means 2 divides 10a+b, i.e. 2 divides b (let 10a+b=2k and solve for b). Hence b=0,2,4,6,8

Is there a way to show that the fact that all even numbers end in 0,2,4,6, or 8 implies the definition of an even number ([tex]n=2k[/tex], where [tex]k[/tex] is an integer)?

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