+177 Find the least positive four-digit solution to the following system of congruences.
\(\begin{align*} 7x &\equiv 21 \pmod{14} \\ 2x+13 &\equiv 16 \pmod{9} \\ -2x+1 &\equiv x \pmod{25} \\ \end{align*}\)
+177 Is the LaTeX not working?
\(x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\)
(Test)
The 3 congruences can be re-written as follows:
x mod 2 =1,
x mod 9 =6,
x mod 25 =17, solve for x
Using CRT plus MMI
i=0;j=0;m=0;t=0;a=(2, 9, 25);r= (1, 6, 17);c=lcm(a); d=c / a[i];n=d % a[i] ;loop1:m++; if(n*m % a[i] ==1, goto loop, goto loop1);loop:s=(c/a[i]*r[j]*m);i++;j++;t=t+s;m=0;if(i< count a, goto4,m=m);printc,"m + ",t % c;return
x =450m + 267, where m=0, 1, 2, 3.........etc.
x =(450 x 2) + 267
x =1167 - This is the least 4-digit solution.
