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load("number-theory.sage")
#####
# Chinese Remainder Theorem tests
a_i = [5, 3, 10]
m_i = [7, 11, 13]
M = 1001
assert crt(a_i, m_i, M) == 894
a_i = [3, 8]
m_i = [13, 17]
M = 221
assert crt(a_i, m_i, M) == 42
#####
# gcd, using Binary Euclidean algorithm tests
assert gcd(21, 12) == 3
assert gcd(1_426_668_559_730, 810_653_094_756) == 1_417_082
#####
# Extended Euclidean algorithm tests
assert egcd(7, 19) == (1, -8, 3)
#####
# Inverse modulo N tests
assert inv_mod(7, 19) == 11