3

p=11
a=8
sum =0
h=(p-1)/2
for k in [1..h]:
    if k*a/p-floor(k*a/p)>1/2:
        sum += 1
print legendre_symbol(a,p)==(-1)^sum

sum

int(mod(32,11))+3

mod(32,11)>5

legendre_symbol(5,29)

for k in [1..14]:
    if mod(k^2,29)==5:
        print k, k^2

173.is_prime()

p = 17
a = 2
val = 0
h = (p-1)/2
for k in [1..h]:
    if mod(k^2,p) == a:
        val = 1
print val

legendre_symbol(7,11)

sigma(9)

sigma(100)

sigma(32)

def mif(f,n):
    sum = 0 
    for d in n.divisors():
        sum += moebius(d)*f(n/d)
    return sum

mif(sigma,4)

def sq(n):
    return n^2

mif(sq,7)

mif(sq,2)

mif(sq,75)

p=107
a=6
sum=0
for k in [1..(p-1)]:
    sum += legendre_symbol(k,p)
sum    

133.is_prime()   

d=210
l = 10
n=100
P=Primes()
for k in range(n):
    val =P.unrank(k)
    start=val
    tVal = True
    for m in [1..(l-1)]:
        val += d
        tVal *= val.is_prime()
    if tVal:
        print start

7
37
67
97
127
127.is_prime()

199+9*210

2089.is_prime()

400-121

factor(279)

(109+1)/2

2*54*55

5940^2+109^2

sqrt(35295481 )

4892*11

legendre_symbol(23,29)

n= 29*37

n

x=100
y=mod(100^13,n)
y

mod(618^853,1073)