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Demonstraţi că suma nr ab*+ba*+123 se divide cu 11.

* nr cu bara deasupra


Răspuns :

ab+ba+132=10a+b+10b+a+132=11a+11b+11*12=11*(a+b+12) | 11
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ab+ba+132 =

=10a+b+10b+a+11
·12

=11a+11b+11·12

=11(a+b+12) | 11