sage: gcd(24, 35)
1
sage: xgcd(24, 35)
(1, -16, 11)
sage: 24*(-16) + 35*11
1

sage: mod(123,35)
18
sage: mod(24^(-1),35) # multiplicative inverse
19

sage: n = randint(10^30,10^31)
sage: n
7784491264756418221413430314892
sage: is_prime(n)
False
sage: factor(n)
2^2 * 19 * 101 * 2897 * 4049 * 28591 * 77527 * 39004675877

sage: mod(123^1098209812309823,34)
...
FloatingPointError: Floating point exception
sage: mod(123,34)^1098209812309823
13

sage: mod(2,7).multiplicative_order()
3
sage: mod(3,7).multiplicative_order()
6
sage: primitive_root(7)
3

sage: legendre_symbol(8,101)
-1

sage: continued_fraction(113/23)
[4; 1, 10, 2]
sage: continued_fraction(sqrt(2))
[1; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, ...]