Question: Order the steps to produce a solution by back substitution of the congruences x 3 (mod 6), x 2 (mod 5), and x 4 (mod

Order the steps to produce a solution by back substitution of the congruences x 3 (mod 6), x 2 (mod 5), and x 4 (mod 7).

Solve this congruence to obtain t= 4 (mod 5) and form the equation f= 5u + 4. Substitute the equation for x in terms of u into the final congruence to yield 30u + 27 = 4 (mod 7). Solve this congruence to obtain u = 6 (mod 7). Substitute the equation for t into the first equation to obtain x = 6(5u + 4)+ 3 =30u + 27 Convert to a congruence to obtain the solution x = 207 (mod 210). Form the equation x = 6f + 3 from the first congruence. Substitute this into the second congruence to yield 6f+ 3 =2 (mod 5). Translate the last congruence into uv = 7v + 6. Substitute the expression for u into the last equation we found for x to obtain x = 210v + 207

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock