how to approach this question by using chinese remainder theorem
Chinese remainder doubt
hello @divesh2000
a number is divisible by 6060 if and only if it is divisible by 33 and 2020.
A number is divisible by 33 if and only if the sum of its digits is divisible by 33. Note that as the sum doesn’t change if we reorder digits, it applies also to the sum of digits of ss.
A number is divisible by 2020 if it ends in 2020, 4040, 6060, 8080 or 0000. Hence, it is necessary and sufficient if ss contains a 00 and then at least one additional even digit.
Overall, there are three conditions to check:
- The digit sum is divisible by 33.
- There is at least a single 00.
- There are at least two even digits (including 00s).
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I understand, the logic but the problem is that in this question where we applied the chinese remainder theorem ??
please let me know.
the statement we said that if number is divisible by 33 and 2020 then it is also divisible by 6060 holds only because of chinese remainder theorem (see highlighted part).
so we have already applied the theorem to reach to those three conditions.
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this statement saying that x%3,x%5,x%4 and x%60 results same answer?
yes if x%3 ==0 and x%5==0 and x%4==0
then using this theorem we can say that x%60 is also going to be 0.
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Thank you bhai for support
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