can the following numbers $23,45326,56740,16320$ be written as a sum of two squares,explain!!!

Question

anonymous · Answer

this are 4 seperate numbers ,NOT one number

whpalmer4 · Answer

At least one of them can be.  Are there any restrictions on what we are squaring?

whpalmer4 · Answer

For example, you can write 23 as

$$23=(\frac{5}{2})^2 + (\frac{\sqrt{67}}{2})^2$$ if you allow the numbers to be any reals...

whpalmer4 · Answer

if you only allow integers, however, then the answer is that 23 cannot be written as the sum of two squares.

anonymous · Answer

we are squaring integers here ,forgot to mention that

anonymous · Answer

so the first thing i see in most questions ,is testing wether the number is Gaussian prime,

$n\equiv 2,3 \mod 4$ gaussian prime  ,$ n\equiv 1 \mod 4$ not gaussian prime

anonymous · Answer

actually for primes ,not just any $n$,also the condition is the other way around,meaning if$p\equiv 1\mod 4 $ then $p$ is not just an ordianry prime but gaussian prime,hence the prime can be written as a sum of two squares,i am interested in factorising this numbers