Thursday, 21 April 2016

elementary number theory - System of Linear Congruences

Find all x such that



\begin{align} x&\equiv 1 \pmod {12}\\ x&\equiv 4 \pmod {21}\\ x&\equiv 18 \pmod {35} \end{align}



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).

No comments:

Post a Comment

real analysis - How to find lim_{hrightarrow 0}frac{sin(ha)}{h}

How to find \lim_{h\rightarrow 0}\frac{\sin(ha)}{h} without lhopital rule? I know when I use lhopital I easy get $$ \lim_{h\rightarrow 0}...