So find the smallest positive integer x such that . The answer should be . (I worked it out using Excel. )
Here is a non-excel solution. First .
Thus, this is equivalent to,
Which gets simplified to,
The first and third congruences combine since .
In first congruence subtract 20 once, in second congruence subtract 9 three times. To get*,
Thus, .
*)You can use Chinese Remainder Theorem here, but I do not like to use that theorem, it is too computational. What you see here is my approach to combining modolus.