<s>[INST] Is $a$ or $b \equiv 0 \pmod{5}$ if $a^2-b^2 \equiv 0 \pmod{5}$? I have this question, knowing the last in title can i define that at least a or b is divisible by 5?
 [/INST] Note that $0 = a^2-b^2 = (a+b)(a-b)$, so either $a-b \equiv 0 \pmod{5}$ or $a+b \equiv 0 \pmod{5}$

UPDATE
So you are saying $a^2 \pmod{5} = b^2 \pmod{5} = 4$. If $a$ is divisible by $5$, so is $a^2$, so since $a^2 \pmod{5} = 4 \ne 0$, you see that $a$ is not divisible by $5$. Similarly, neither is $b$.
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