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Lecture 11
Lecture 11

... In the above example, the local variable sum is reinitialized to zero in each recursive call (each call has its own sum). Hence, the returned value is 0. One correct solution is: int sumFirst_n_PositiveInts(int n) { if(n == 1) return n; else return n + sumFirst_n_PositiveInts(n – 1); ...
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... It begs to differ, however, that if the recipient makes m  pq public so that the value of m is known to the world, how does this prevent an intruder discovering what the primes p and q are? Well, the answer comes down to this fact: It is much easier to find primes p and q and form m  pq then it is ...
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Review for Test #4- Exponential and Log Functions

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Addition



Addition (often signified by the plus symbol ""+"") is one of the four elementary, mathematical operations of arithmetic, with the others being subtraction, multiplication and division.The addition of two whole numbers is the total amount of those quantities combined. For example, in the picture on the right, there is a combination of three apples and two apples together; making a total of 5 apples. This observation is equivalent to the mathematical expression ""3 + 2 = 5"" i.e., ""3 add 2 is equal to 5"".Besides counting fruits, addition can also represent combining other physical objects. Using systematic generalizations, addition can also be defined on more abstract quantities, such as integers, rational numbers, real numbers and complex numbers and other abstract objects such as vectors and matrices.In arithmetic, rules for addition involving fractions and negative numbers have been devised amongst others. In algebra, addition is studied more abstractly.Addition has several important properties. It is commutative, meaning that order does not matter, and it is associative, meaning that when one adds more than two numbers, the order in which addition is performed does not matter (see Summation). Repeated addition of 1 is the same as counting; addition of 0 does not change a number. Addition also obeys predictable rules concerning related operations such as subtraction and multiplication.Performing addition is one of the simplest numerical tasks. Addition of very small numbers is accessible to toddlers; the most basic task, 1 + 1, can be performed by infants as young as five months and even some non-human animals. In primary education, students are taught to add numbers in the decimal system, starting with single digits and progressively tackling more difficult problems. Mechanical aids range from the ancient abacus to the modern computer, where research on the most efficient implementations of addition continues to this day.
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