Difference between revisions of "Talk:Legendre theorem"
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| − | The original notation $x^2\equiv-bc\pmod{|a|},x^2\equiv-ca\pmod{|b|},x^2\equiv-ab\pmod{|c|}$ was not helpful as the $x$ involved is not the same in the three congruences, nor is it the same as the $x$ in $ax^2+by^2+cz^2=0$. The revision is also confusing as the $x,y,z$ in the initial equation are not the same as the $x,y,z$ in the congruences. In words, each condition should simply read $-bc$ ''is a square modulo'' $|a|$, etc. [[User:Richard Pinch|Richard Pinch]] ([[User talk:Richard Pinch|talk]]) 10: | + | The original notation $x^2\equiv-bc\pmod{|a|},x^2\equiv-ca\pmod{|b|},x^2\equiv-ab\pmod{|c|}$ was not helpful as the $x$ involved is not the same in the three congruences, nor is it the same as the $x$ in $ax^2+by^2+cz^2=0$. The revision is also confusing as the $x,y,z$ in the initial equation are not the same as the $x,y,z$ in the congruences. In words, each condition should simply read $-bc$ ''is congruent to a square modulo'' $|a|$, etc. [[User:Richard Pinch|Richard Pinch]] ([[User talk:Richard Pinch|talk]]) 10:30, 20 August 2016 (CEST) |
Latest revision as of 08:30, 20 August 2016
Notation
The original notation $x^2\equiv-bc\pmod{|a|},x^2\equiv-ca\pmod{|b|},x^2\equiv-ab\pmod{|c|}$ was not helpful as the $x$ involved is not the same in the three congruences, nor is it the same as the $x$ in $ax^2+by^2+cz^2=0$. The revision is also confusing as the $x,y,z$ in the initial equation are not the same as the $x,y,z$ in the congruences. In words, each condition should simply read $-bc$ is congruent to a square modulo $|a|$, etc. Richard Pinch (talk) 10:30, 20 August 2016 (CEST)
How to Cite This Entry:
Legendre theorem. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Legendre_theorem&oldid=39046
Legendre theorem. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Legendre_theorem&oldid=39046