Thursday, 21 April 2016

elementary number theory - System of Linear Congruences

Find all x such that



x1(mod12)x4(mod21)x18(mod35)



Im not quite sure if this system of linear congruence is solvable. Since

gcd(12,21)=3, gcd(12,35)=1 and gcd(21,35)=7, and the CRT states that "If(m1, m2) = 1, then the system has its complete solution a single resident class (mod m1.....mr).

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