MHB Discover All Possible 8-Digit Multiples of 2013 with $A = \overline{20abcd13}$

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The discussion focuses on finding all possible 8-digit numbers of the form $A = \overline{20abcd13}$ that are multiples of 2013. Participants explore the constraints imposed by the structure of $A$ and the divisibility rule for 2013. The calculations involve determining the range of values for the digits $a$, $b$, $c$, and $d$ that satisfy the multiple condition. The conversation emphasizes the importance of modular arithmetic in narrowing down the valid combinations. Ultimately, the goal is to identify all valid 8-digit multiples of 2013 fitting the specified format.
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$A=\overline{20abcd13}$ is an 8-digit number ,

also $A$ is a multiple of 2013,please find all possible value of $A$
 
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we know 20132013 multiple of 2013
as 20abcd13 = 20132013 + 201300 * x
so the soultions are 20132013 + 201300 * x as last 2 digits are 13
x= 0 gives 20132013
x =1 gives 20333313
x=2 gives 20534613
x=3 gives 20735913
x=4 gives 20937213
x >=5 gives value outside range
 
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