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Demonstrati ca daca 10|(3a+7b),atunci 10|(7a+3b)​

Răspuns :

[tex]\displaystyle\it\\10|(10a+10b),~evident.\\dar,~10|3a+7b,~scazand~cele~doua~relatii,~obtinem~:~\\10|\Big((10a+10b)-(3a+7b)\Big)=(7a+3b),~deci~,10|(7a+3b)[/tex]

10 | 10a+10b
10 | 3a+7b (-)
=> 10 | (10a+10b) - (3a+7b)
=> 10 | (7a+3b)