Problem: Because a linear combination with integer coefficients of algebraic integers is again an algebraic integer , this proves the statement .
Since a linear combination with integer coefficients of algebraic integers is an algebraic integer , this proves the statement .
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A: yes

Problem: The next day Mount Dana was climbed by the group before Muir had to return to Martinez .
Mount Dana , elevation , was climbed the next day by the group before Muir had to return home to Martinez .
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A: yes

Problem: The Banaue rice terraces were declared National Cultural Treasure by the Philippine government under the name of Ifugao Rice Terraces by Presidential Decree No . 260 in 1973 .
The Banaue Rice Terraces were declared by the Philippine government as a National Cultural Treasure under Ifugao Rice Terraces by virtue of Presidential Decree No . 260 in 1973 .
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A:
yes