Prove or disprove: if a^2=b^2=mod(n) and n is prime then a=b(mod n) or a=-b(mod n).
True: $\displaystyle a^2=b^2\!\!\!\pmod n \Longleftrightarrow (a-b)(a+b)=0\!\!\!\pmod n$ $\displaystyle \Longleftrightarrow a-b=0\!\!\!\pmod n\,\,\,or\,\,\,a+b=0\!\!\!\pmod n$ , since n is prime.