Need some help with this one: can anybody help solve this problem. Can 15! be written as the sum of at least 3 squares? If so, what are the numbers? Any help or hint would be great. Thank you.

Guest Jan 10, 2019

#2**+1 **

Are you studying Number Theory? ALMOST all numbers can be written as a sum of 3 squares, with some exceptions. However, ALL numbers can be written as sum of 4 squares. There is a difficult proof of 3-square theorem by the French mathematician A.-M. Legendre in 1770. There are also special computer programs that will calculate this for you. I wrote one just to see if I could solve your particular problem. I was able to solve it using C++. Here is your answer:

**15! =1,307,674,368,000 = 1,022,752² + 511,520² + 64²**

Guest Jan 11, 2019

#1**+1 **

I don't know how this works but I can give you a litte info!

15! also equals = 1, 307, 674, 368, 000

APatel Jan 10, 2019

#2**+1 **

Best Answer

Are you studying Number Theory? ALMOST all numbers can be written as a sum of 3 squares, with some exceptions. However, ALL numbers can be written as sum of 4 squares. There is a difficult proof of 3-square theorem by the French mathematician A.-M. Legendre in 1770. There are also special computer programs that will calculate this for you. I wrote one just to see if I could solve your particular problem. I was able to solve it using C++. Here is your answer:

**15! =1,307,674,368,000 = 1,022,752² + 511,520² + 64²**

Guest Jan 11, 2019