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November 24th, 2017, 12:27 PM   #1
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10 years old math problem - please help me solve it

a, b, c are natural numbers and ab(a+b)+ac(a+c)+bc(b+c)=2013. To choose the correct value for product axbxc.
A) 2013
B) 620
C) 324
D) 0
E) other number

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November 24th, 2017, 01:28 PM   #2
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Are you sure you typed the equation correctly?

The expression ab(a+b)+ac(a+c)+bc(b+c) always has an even value, so it can't equal 2013.
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November 24th, 2017, 01:48 PM   #3
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Yes, I'm sure that this is the request.
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November 24th, 2017, 03:17 PM   #4
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If a is even, then ab and ac are even and thus so are ab(a + b) and ac(a + c). So that sum is even. If either b or c is even, then bc is even as is bc(b + c). If neither b nor c is even, then b + c is even and so is bc(b + c). In short, if a is even, that sum is even no matter what b and c are.

But we could do the same analysis for b and for c.

So lets suppose a, b, and c is odd. Then (a + b), (a + c), and (b + c) are all even, so the sum is even.

As skipjack said, there is no way that the sum can equal 2013.
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