$x^3 \equiv x(mod$ $3)$ for all x, whereas obviously $x^3$ and $x$ are not algebraically congruent $(mod$ $3)$. What does it mean to be algebraically congruent?. In this case the two polynomials can be viewed as $x^3+0x^2+0x+0 \equiv 0x^3+0x^2+x+0$, so for example the coefficients for $x^3$ are 1 and 0 which are not congruent $(mod$ $3)$. Is that right?

• If you're following a text, what does that text define as two polynomials being algebraically congruent? – coffeemath Jul 3 '16 at 23:02
• two polynomials g and f are congruent if the coefficients of each power of x in g and f are congruent (mod m). The text never mentions the word "algebraically" in the definitions, so I infer that's the right definition. – TheMathNoob Jul 3 '16 at 23:03
• TheMathNoob In your last comment, what the definition is gives exactly what you spelled out before the final "Is that right?" question. OH, I guess your issue is with the extra qualifier "algebraically"... hard to guess what text intends but I'd guess same as without it. – coffeemath Jul 3 '16 at 23:05
• That's what I think it is. – TheMathNoob Jul 3 '16 at 23:06