Răspuns :
abcabc in baza 10 = 100000a+10000b+1000c+100a+10b+c
=100100a+10010b+1001c
=1001(100a+10b+c) Adevarat
=100100a+10010b+1001c
=1001(100a+10b+c) Adevarat
abcabc = 100000a + 10000b + 1000c + 100a + 10b + c = 100100a + 10010b + 1001c. Se da factor comun 1001.
1001(100a + 10b + c), care se imparte exact la 1001, rezulta ca abcabc se imparte exact la 1001.
1001(100a + 10b + c), care se imparte exact la 1001, rezulta ca abcabc se imparte exact la 1001.