i suppose this is the correct place to post this question...it is easy to prove that 2 different pairs of Natural numbers cannot have the same sum AND the same product.Can this be proven for groups of 3,4,5,...n Natural numbers?

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- Nov 16th 2011, 11:23 AMLasombrasums and products...
i suppose this is the correct place to post this question...it is easy to prove that 2 different pairs of Natural numbers cannot have the same sum AND the same product.Can this be proven for groups of 3,4,5,...n Natural numbers?

- Nov 16th 2011, 06:06 PMMonroeYoderRe: sums and products...
For 2 different pairs of natural numbers we can do it without much difficulty. Let our pairs be and and remember these sets are not equal.

Suppose that and . Since we can say for some non-zero number

To ensure we then know that

Then and since we know that we must have

So by factoring we have . Remember that and so which means

Therefore and

Therefore but this is a contradiction. So two different pairs of natural numbers cannot have both the same sum and same product. - Nov 17th 2011, 03:36 AMOpalgRe: sums and products...