2025/014) Show that there are infinitely many positive integers which cannot be expressed as the sum of squares.

we have $n^2 \equiv 0/1 \pmod 4$

So $m^2 + n^2 \equiv 0/1/2 \mod 4$

So any number of  of the form 4k + 3 cannot be expressed as sum of 2 squares

There are infinitely many of them 

Hence proved