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The law of quadratic reciprocity 'or' statement

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I have just seen written that $(frac17101)$ = $(frac10117)$. But doesn't the law of quadratic reciprocity state that $(fracpq)$ = $(fracqp)$ if $pequiv1 mod 4$ OR $qequiv1mod4$?

number-theory modular-arithmetic legendre-symbol

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asked yesterday

JlatmerJlatmer

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  $begingroup$
  In mathematics, "or" is almost always inclusive, so we allow for both conditions to hold.
  $endgroup$
  – Wojowu
  yesterday
  
  

  
  
  
  

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0

$begingroup$

I have just seen written that $(frac17101)$ = $(frac10117)$. But doesn't the law of quadratic reciprocity state that $(fracpq)$ = $(fracqp)$ if $pequiv1 mod 4$ OR $qequiv1mod4$?

number-theory modular-arithmetic legendre-symbol

share|cite|improve this question

asked yesterday

JlatmerJlatmer

64

$endgroup$

• 
  
  
  

  
  7
  

  
  
  
  
  
  

  
  $begingroup$
  In mathematics, "or" is almost always inclusive, so we allow for both conditions to hold.
  $endgroup$
  – Wojowu
  yesterday
  
  

  
  
  
  

add a comment | 

$begingroup$

I have just seen written that $(frac17101)$ = $(frac10117)$. But doesn't the law of quadratic reciprocity state that $(fracpq)$ = $(fracqp)$ if $pequiv1 mod 4$ OR $qequiv1mod4$?

number-theory modular-arithmetic legendre-symbol

share|cite|improve this question

asked yesterday

JlatmerJlatmer

64

$endgroup$

share|cite|improve this question

asked yesterday

JlatmerJlatmer

64

share|cite|improve this question

asked yesterday

JlatmerJlatmer

64

asked yesterday

JlatmerJlatmer

64

asked yesterday

JlatmerJlatmer

64