Cornachia’s algorithm can be adapted to the case of the equation x2+dy2=nand even to the case of ax2+bxy+cy2=n. For the sake of completeness, we have given modalities without proofs (the proof in the case of the equa...Cornachia’s algorithm can be adapted to the case of the equation x2+dy2=nand even to the case of ax2+bxy+cy2=n. For the sake of completeness, we have given modalities without proofs (the proof in the case of the equation x2+y2=n). Starting from a quadratic form with two variables f(x,y)=ax2+bxy+cy2and n an integer. We have shown that a primitive positive solution (u,v)of the equation f(x,y)=nis admissible if it is obtained in the following way: we take α modulo n such that f(α,1)≡0modn, u is the first of the remainders of Euclid’s algorithm associated with n and α that is less than 4cn/| D |) (possibly α itself) and the equation f(x,y)=n. has an integer solution u in y. At the end of our work, it also appears that the Cornacchia algorithm is good for the form n=ax2+bxy+cy2if all the primitive positive integer solutions of the equation f(x,y)=nare admissible, i.e. computable by the algorithmic process.展开更多
RIASSUNTO-In due aree della città di Brescia si è accertata la presenza non occasionale di Cornacchiegrigie.Queste aree sono localizzate a nord ed a ovest(dove è stata rilevata la presenza di un nido)de...RIASSUNTO-In due aree della città di Brescia si è accertata la presenza non occasionale di Cornacchiegrigie.Queste aree sono localizzate a nord ed a ovest(dove è stata rilevata la presenza di un nido)del centro storico della città.La presenza delle Cornacchie è simile nelle due aree di studio e varia infunzione della stagione e della presenza umana.L’Autore discute il vantaggio adattativo di tale colonizza-zione,anche se il limite imposto dall’esiguo numero di soggetti per ora presenti impone cautela nell’inter-pretazione dei dati.First data on the presence of Hooded Crows Corvus corone cornix in Brescia(NorthernItaly).Two areas near the centre of the town of Brescia were kept under observation in the courseof the day and of the year to ascertain the non occasional presence of hooded crows.These areas arelocalized north and west from the centre of the town.The number of Hooded Crows is similar in bothareas but,throughout the year,it fluctuates with seasons and human presence.A nest presence hasbeen ascertained in the western area were the animals are more regularly present throughout the year.I argue the adaptive advantage of this colonization.展开更多
文摘Cornachia’s algorithm can be adapted to the case of the equation x2+dy2=nand even to the case of ax2+bxy+cy2=n. For the sake of completeness, we have given modalities without proofs (the proof in the case of the equation x2+y2=n). Starting from a quadratic form with two variables f(x,y)=ax2+bxy+cy2and n an integer. We have shown that a primitive positive solution (u,v)of the equation f(x,y)=nis admissible if it is obtained in the following way: we take α modulo n such that f(α,1)≡0modn, u is the first of the remainders of Euclid’s algorithm associated with n and α that is less than 4cn/| D |) (possibly α itself) and the equation f(x,y)=n. has an integer solution u in y. At the end of our work, it also appears that the Cornacchia algorithm is good for the form n=ax2+bxy+cy2if all the primitive positive integer solutions of the equation f(x,y)=nare admissible, i.e. computable by the algorithmic process.
文摘RIASSUNTO-In due aree della città di Brescia si è accertata la presenza non occasionale di Cornacchiegrigie.Queste aree sono localizzate a nord ed a ovest(dove è stata rilevata la presenza di un nido)del centro storico della città.La presenza delle Cornacchie è simile nelle due aree di studio e varia infunzione della stagione e della presenza umana.L’Autore discute il vantaggio adattativo di tale colonizza-zione,anche se il limite imposto dall’esiguo numero di soggetti per ora presenti impone cautela nell’inter-pretazione dei dati.First data on the presence of Hooded Crows Corvus corone cornix in Brescia(NorthernItaly).Two areas near the centre of the town of Brescia were kept under observation in the courseof the day and of the year to ascertain the non occasional presence of hooded crows.These areas arelocalized north and west from the centre of the town.The number of Hooded Crows is similar in bothareas but,throughout the year,it fluctuates with seasons and human presence.A nest presence hasbeen ascertained in the western area were the animals are more regularly present throughout the year.I argue the adaptive advantage of this colonization.
