Wednesday, 9 September 2015

number theory - Find all solutions to the system $x equiv 1 pmod 4, x equiv 0 pmod 3$, and $x equiv 5 pmod 7$

Find all solutions to the congruences x $\equiv$ 1 (mod 4), x $\equiv$ 0 (mod 3), and x $\equiv$ 5 (mod 7). I got $M =m_1 * m_2 * m_3 = 4*3*7 = 84$



$M_1 = 21, M_2 = 28, M_3 = 12$



So I get $x = 21*u + 28*v + 12*w$



Now I don't know how to get $u, v$, and $w$. I know that I am supposed to use Chinese Remainder Theorem and Euler's algorithm but I don't know how to use them here. Can someone please help me. Or suggest me something easier.

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