condition can be derived by substituting the general solution of the middle equation in (3) to the last equation. The result is <span class="nowrap">g<sub>3</sub>|(R<sub>1</sub>-R<sub>2</sub>)</span>, where <span class="nowrap">g<sub>3</sub>=gcd(60A,U)</span>. To sum up, the system of congruence equations in (3) has a solution iff</p><p>60g<sub>1</sub>|(R<sub>1</sub>-TR<sub>0</sub>),&nbsp;&nbsp;<span class="nowrap">g<sub>2</sub>|(R<sub>2</sub>-R<sub>0</sub>T)</span>,&nbsp;&nbsp;<span class="nowrap">g<sub>3<