Expressing Squared Numbers as Product of Two Consecutive Odd or Even Natural Numbers

It turns out that you can write almost any squared number in terms of the product of two odd or even integers plus one. As an example, let’s go through the following operation:

29 * 31 = (30 – 1)(30 + 1) = 30^2 – 1  because (a – b)(a + b) = a^2 – b^2

30^2 = 29 * 31 + 1

So as you can see here, you can write 30^2 as the product of two consecutive odd natural numbers, 29 and 31 and add 1 to the product. You can do this with almost every square number. I am using the word “almost” here since I have not taken the time to test every possible case not have I proved this nor have I seen a proof for it.

Wherever this happens to come in handy depends on the kind of problems you might be solving.

Author: John Raschedian

Web Developer

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