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IMO Shortlist 1972 problem 6

1972 shortlist
Show that for any n \not \equiv 0 \pmod{10} there exists a multiple of n not containing the digit 0 in its decimal expansion.

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1234IMO Shortlist 1966 problem 51
1966 shortlist
0
1235IMO Shortlist 1966 problem 52
1966 shortlist
0
1237IMO Shortlist 1966 problem 54
1966 shortlist
0
1240IMO Shortlist 1966 problem 57
1966 shortlist
0
1259IMO Shortlist 1967 problem 3
1967 shortlist
1
1433IMO Shortlist 1972 problem 3
1972 shortlist
0