SOLUTION: How do you write 17! as the difference of two integer perfect squares? Ms.Ikelyn Provided me a Quora solution here: http://www.algebra.com/tutors/students/your-answer.mpl?ques

Question 1199407: How do you write 17! as the difference of two integer perfect squares?
Ms.Ikelyn Provided me a Quora solution here:
http://www.algebra.com/tutors/students/your-answer.mpl?question=1199406
Thank you Ms.Ikelyn!
I just had one question - would it be correct to write the difference of squares where the squares are actually expressions? Because the quora solution suggests we write it as:
"(17! / 4 + 1)^2 - (17! / 4 - 1)^2"
Please let me know. Here is the quora link:
https://www.quora.com/How-do-you-write-17-as-the-difference-of-two-integer-perfect-squares
Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52767) (Show Source): You can put this solution on YOUR website!
.

Just answered in full under this link

https://www.algebra.com/algebra/homework/word/misc/Miscellaneous_Word_Problems.faq.question.1199406.html

Answer by math_tutor2020(3816) (Show Source): You can put this solution on YOUR website!

The value of 17! is very large.

Using a calculator shows that
17! = 17*16*15*...*3*2*1 = 3.556874 * 10^14
with more precision we have
17! = 355,687,428,096,000

It's roughly 355.7 trillion.

Because of the large value, the expressions
(17!)/4 + 1
(17!)/4 - 1
are also massive.

This means it's much better to leave the expressions as they are; rather than computing them to determine what integer they are equal to.

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