Primitive root of 13

used ETF and gcd

P = ETF(13);

Q = ETF(P);

fprintf("Total roots: %d", Q);

fprintf("\n");

One = mod(2.^12,13);

fprintf("Since 2 to power 12 modular 13 equal to %d, 2 is a primitive root of 13. \n",One);

fprintf("The primitive roots of 13: ");

A = [];

for i = 1:12

d = gcd(i,12);

if(d==1)

result = mod(2.^i,13);

A(end+1) = result;

end

end

A = sort(A);

fprintf("%g ",A);

function res = ETF(N)

S = 1;

for i = 1:N

x = mod(N,i);

if(x==0)

y = isprime(i);

end

if(y==1)

S = S.*(1-1./i);

end

end

res = N.*S;

end

function res = gcd(m,n)

while true

remainder = mod(n,m);

if(remainder == 0)

res = m;

break;

end

n = m;

m = remainder;

end

end