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Q: Two consecutive odd integers have a product of 99 find the larger number?

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Two negative consecutive odd integers that have a product of 63 are -7 and -9. -7 is larger than -9. -7 is the answer.

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A rectangular number is a number which is the product of two consecutive integers.

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I think the answer is zero. The only 15 consecutive integers whose average is 7 are the integers 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14. For any odd number of consecutive integers the average will be equal to the middle number, and this is the only group of 15 consecutive integers with 7 as the middle number. The product of any group of numbers that includes 0 will always be 0 because 0 times anything is 0.

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A square number is the product of the same two integers. A rectangular number is the product of consecutive integers.

If you define a rectangular number as a number which is the product of two consecutive integers, it cannot be square.

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