Chinese Remainder Theorem

[Santanu Sarkar]

I want to find integer such that
x= 1 mod 3
x=2  mod 5
x=3  mod 7
like this system of congruences using Chinese Remainder Theorem.
In Sage, crt() function takes only 4 argument.

[D. S. McNeil]

sage: help(CRT)

crt(a, b, m=None, n=None)
Returns a solution to a Chinese Remainder Theorem problem.

INPUT:

- ``a``, ``b`` - two residues (elements of some ring for which
extended gcd is available), or two lists, one of residues and
one of moduli.
[...]

If ``a`` and ``b`` are lists, returns a simultaneous solution to
the congruences `x\equiv a_i\pmod{b_i}`, if one exists.

.. SEEALSO::

- :func:`CRT_list`

sage: CRT([1,2,3],[3,5,7])
52
sage: x = CRT([1,2,3],[3,5,7])
sage: x % 3, x % 5, x % 7
(1, 2, 3)

Doug

[Santanu Sarkar]

Thank you.

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