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A composite number is one that is neither prime nor 1.
Show that 10201 is composite in any base.
Likewise show that 10101 is composite in any base.
Further Reading: Learn About Number Bases by Toni Beardon
Start with any number of counters in any number of piles. 2 players take it in turns to remove any number of counters from a single pile. The loser is the player who takes the last counter.
Find b where 3723(base 10) = 123(base b).
A collection of games on the NIM theme