91Ó°ÊÓ

Add the hexadecimal numbers. $$ 349 \mathrm{CC}+922 \mathrm{D} $$

Add the hexadecimal numbers. $$ 82054+\text { AEFA3 } $$

Use the following notation and terminology. We let \(E\) denote the set of positive, even integers. If \(n \in E\) can be written as a product of two or more elements in \(E\), we say that \(n\) is \(E\) -composite; otherwise, we say that \(n\) is \(E\) -prime. As examples, 4 is \(E\) -composite and 6 is \(E\) -prime. Find a necessary and sufficient condition for an integer to be an \(E\) -prime. Prove your statement.

In the octal (base 8) number system, to represent integers we use the symbols \(0,1,2,3,4,5,6,\) and \(7 .\) In representing an integer, reading from the right, the first symbol represents the number of I's, the next symbol the number of 8 's, the next symbol the number of \(8^{2}\) 's, and so on. In general, the symbol in position \(n\) (with the rightmost symbol being in position 0 ) represents the number of \(8^{n}\) 's. $$ 7711 $$