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

[Albert1]

$A=\overline{20abcd13}$ is an 8-digit number ,

also $A$ is a multiple of 2013,please find all possible value of $A$

 

[kaliprasad]

Spoiler

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