On the Subject of Chinese Remainder Theorem

“Okay, we got a CRT.”
“Oh ok, those old TVs?”
“No.”
“Huh? ...oh christ.”

On the module will be a blank display, a pressable display that shows information in the form N % a = b, where a and b are integers, and a keypad with a red and a green button.

The red button will be used to clear the input, the green button will be used to submit the input, and the numbered buttons will be used to input digits.

There can be anywhere from 4 to 8 equations of the form N % a = b. Note down all of them, pressing the display to cycle through all equations.

The goal is to find a valid positive integer N such that all modular equations are satisfied.

After finding a valid value N, enter it using the keypad and press the submit button, after which the module will be disarmed. Note that any value greater than 9 digits will not be accepted.

If the wrong value is submitted, a strike will incur and the module will reset.