# Geeky Is Awesome

Students are made to check tips on how to issue polynomials but are never given an interesting task that involves using polynomial factorization. Here’s a use that I find fascinating. It signifies that any number which precedes a square number can at all times be factored into two numbers: one greater than the quantity that was squared and one less than the number that was squared. Are there any numbers preceding a sq. number which are prime numbers? If there’s such a number, then it’s components must be 1 and itself.

1 and the number itself (which is prime). Since “x” is a constructive quantity (the number that is squared), it might only be the “x-1” factor. Three, when “x” is 2 which makes sense since we mentioned that one of many elements have to be 1 and the other should be the quantity itself.

If 3 a main quantity? Therefore 3 is a main number which precedes a sq. quantity. Are there every other prime numbers that precede a sq. quantity? No, as a result of if “x-1” is the rest however 1, then neither of the two components will be 1, making the quantity factorizable into two numbers which aren’t 1 and itself, hence not being a primary quantity. Which means that 2 is the only quantity “x” will be, which means that there aren’t any other numbers that precede a sq. number which can be prime.

It’s interesting to also notice that utilizing the same technique, one can proof that 7 is the only number previous a cube quantity that is prime. Use this website to seek out the components of numbers preceding different powers of “x”. It seems that there can only one number previous an nth power of “x” that can be prime, for every energy of “n”. Can we show this? 0, for all “n”. Such prime numbers are known as Mersenne primes.

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• How Logan got so versatile