:: deftheorem Def4 defines LegendreSymbol NAT_6:def 4 :
for p being natural prime number
for a being integer number holds
( ( a gcd p = 1 & a is_quadratic_residue_mod p implies LegendreSymbol (a,p) = 1 ) & ( p divides a implies LegendreSymbol (a,p) = 0 ) & ( a gcd p = 1 & a is_quadratic_non_residue_mod p implies LegendreSymbol (a,p) = - 1 ) );