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Demonstrati ca numerele de forma abcabc sunt divizibile cu 13.

Răspuns :

abcabc⇒scris in baza 100000⇒abcabc=100000a+10000b+1000c+100a+10b+1c
abcabc=
100000a+10000b+1000c+100a+10b+c=
100100a+10010b+1001c=
13*(7700a+770b+77c)