Prove a square can't be written $5x+ 3$, for all integers $x$. Homework question, should I use induction?.. 
Help please

Hint $\ $ Let $\,n\,$ by any integer. $\ {\rm mod}\ 5\!:\ n \equiv 0,\pm1,\pm2\,\Rightarrow\, n^2\equiv 0,1,4,\,$ so  $\ n^2\not\equiv 3\!\pmod{\!5}$
Remark $ $ It's easier if you know $\mu$Fermat: $\ 3 \equiv n^2\overset{\rm square}\Rightarrow\color{#0a0}{-1}\equiv \,n^4\ [\,\equiv \color{#c00}1$ by $\mu$Fermat]
This is a special case of Euler's Criterion: $\,{\rm mod}\ p=5\!:\,\ 3 \not\equiv n^2\, $ by $\ 3^{(p-1)/2}\equiv\color{#0a0}{-1}\not\equiv \color{#c00}1$
