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- Thread starter willr12
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- #1

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- #2

mfb

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If you can use or prove the formula for the triangular numbers, sure.

- #3

Mark44

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x

= x(x

= x(x - 1)(x + 1) - y(y - 1)(y+ 1)

In a more suggestive form, the last expression is

(x - 1)(x)(x + 1) - (y - 1)(y)(y + 1), with each group being the product of three successive integers.

It's not too hard to show that the product of three integers in succession is divisible by 6 (can do this by induction), so the difference of two such products is also divisible by 6.

- #4

mfb

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Or splitting it into 5 to 6 cases.(can do this by induction)

That is the more elementary approach if the triangle formula is not available.

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