Created
October 10, 2022 20:42
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| const gcd = (a,b) => xcgd(a,b)[0] | |
| function xcgd(a,b){ | |
| if(a==0) | |
| return [b,0,1] | |
| var result = xcgd( b%a ,a) | |
| var x = result[2]- parseInt(b/a)*result[1] | |
| var y = result[1] | |
| return [result[0],x,y] | |
| } | |
| function modinverse(a,m){ | |
| for(var x=1;x<m;x++){ | |
| if( ( (a%m)*(x%m) ) %m ==1) | |
| return x | |
| } | |
| return 1 | |
| } | |
| function primeFactors(n) { | |
| const factors = []; | |
| let divisor = 2; | |
| while (n >= 2) { | |
| if (n % divisor == 0) { | |
| factors.push(divisor); | |
| n = n / divisor; | |
| } else { | |
| divisor++; | |
| } | |
| } | |
| return factors; | |
| } | |
| function powerMod(base, exponent, modulus) { | |
| if (modulus === 1) return 0; | |
| var result = 1; | |
| base = base % modulus; | |
| while (exponent > 0) { | |
| if (exponent % 2 === 1) //odd number | |
| result = (result * base) % modulus; | |
| exponent = exponent >> 1; //divide by 2 | |
| base = (base * base) % modulus; | |
| } | |
| return result; | |
| } | |
| function coprime(a){ | |
| cont=0 | |
| for(var c=1;c<=a;c++){ | |
| if(gcd(c,a)==1) | |
| cont++ | |
| } | |
| return cont | |
| } | |
| try{ | |
| log("gcd (5,6)="+gcd(5,6)) | |
| log("gcd (8,16)="+gcd(8,16)) | |
| log("xgcd (35,15)="+xcgd(35,15)) | |
| var result= xcgd(35,15) | |
| var r= result[0] | |
| var p= result[1] | |
| var q= result[2] | |
| log("r,p,q =xgcd (35,15); r= gcd =35*p+15*q "+ ( gcd(35,15)== p*35+q*15 ) ) | |
| log("coprime(5)="+coprime(5)) | |
| log("coprime(6)="+coprime(6)) | |
| log("coprime(7)="+coprime(7)) | |
| log("coprime(8)="+coprime(8)) | |
| log("primeFactors(5578)="+primeFactors(2196).join(" ")) | |
| log("modinverse(3,11)="+modinverse(3,11)) | |
| log("modinverse(352,917)="+modinverse(352,917)) | |
| log("power mod(15, 831, 23)="+powerMod(15, 831, 23)) | |
| /* | |
| gcd (5,6)=1 | |
| gcd (8,16)=8 | |
| xgcd (35,15)=5,1,-2 | |
| r,p,q =xgcd (35,15); r= gcd =35*p+15*q true | |
| coprime(6)=2 | |
| coprime(7)=6 | |
| coprime(8)=4*/ | |
| }catch(e){ | |
| console.log(e) | |
| } | |
| function log(a) { | |
| document.getElementsByTagName("body")[0].innerHTML+=a+"<br>" | |
| } |
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