Chapter 15 Appendix F - Simultaneous Linear congruences

Practice solving simultaneous linear congruences

Consider simultaneous linear congruences \[ a_1x \equiv b_1\text{ mod }(n_1),\; a_2x \equiv b_2\text{ mod }(n_2),\; a_3x \equiv b_3\text{ mod }(n_3). \] Pick integer values for \(a_i,b_i\) and \(n_i\), and use the Chinese Remainder Theorem to check for a solution to the congruence.

As an example, try the following values

Now check your answers by entering your values of \(a_i,b_i\) and \(n_i\) in the boxes below and hit the “Solve Congruences” button.

 

a₁ b₁ n₁

a₂ b₂ n₂

a₃ b₃ n₃