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 Jun 26 awarded Notable Question Dec 5 accepted Is $20+k^2\not\equiv4(\text{mod}~7)$ for all $k\geq0$? Dec 5 awarded Custodian Dec 5 reviewed Approve Is $20+k^2\not\equiv4(\text{mod}~7)$ for all $k\geq0$? Dec 5 comment Is $20+k^2\not\equiv4(\text{mod}~7)$ for all $k\geq0$? How come adding 2 to $k^2$ makes the statement true, but when you just use $k^2$ the statement is false? (ie. $k^2$ is 0 modulo 7 but 2 + $k^2$ is NOT 0 modulo 7) Why does the 2 have this effect? Dec 5 asked Is $20+k^2\not\equiv4(\text{mod}~7)$ for all $k\geq0$? Jul 19 awarded Popular Question Jul 18 awarded Nice Question Jul 18 awarded Supporter Jul 18 comment Proof: For all integers $x$ and $y$, if $x^3+x = y^3+y$ then $x = y$ You could even just say that (x^2+y^2+xy+1) =/= 0, and conclude x-y = 0, and thus x=y, correct? Anyway, thank you for your help! Jul 18 accepted Proof: For all integers $x$ and $y$, if $x^3+x = y^3+y$ then $x = y$ Jul 18 asked Proof: For all integers $x$ and $y$, if $x^3+x = y^3+y$ then $x = y$ May 31 awarded Scholar May 31 accepted How to simplify this rational expression? May 30 awarded Student May 30 asked How to simplify this rational expression?