load("number-theory.sage")

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# Chinese Remainder Theorem tests
a_i = [5, 3, 10]
m_i = [7, 11, 13]
assert crt(a_i, m_i) == 894

a_i = [3, 8]
m_i = [13, 17]
assert crt(a_i, m_i) == 42


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# 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

assert gcd_recursive(21, 12) == 3

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# Extended Euclidean algorithm tests
assert egcd(7, 19) == (1, -8, 3)
assert egcd_recursive(7, 19) == (1, -8, 3)

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# Inverse modulo N tests
assert inv_mod(7, 19) == 11