I have seen this small equality used in a proof that I was reading and I wanted to show that it is true. It seems like an easy problem but I didn't know how to start. Can you show me how is it true?
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Let $a = k\cdot m + b$ where $0< b \le m-1$, and try writing out both sides. – desiigner Aug 22 '19 at 02:29
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1It seems that this is telling you that if $b=a \mod m$, then $b^2=a^2 \mod m$. – Julian Mejia Aug 22 '19 at 02:31
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Thanks to both of you, I solved the problem by using letting $a = km + b$. – user666150 Aug 22 '19 at 02:38
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The language “$a$ mod $m = b$" is poorly suited to mathematical statements, as your title shows. So much better to use the mathematical notation “$a\equiv b\pmod m$”, as @JulianMejia hints. – Lubin Aug 22 '19 at 04:54