Mathathon Round 1 (2 points each) 1. This year, the Mathathon
... multiple of 5. Thus, y = 0. By the bound xyz(t + 1) ≤ 10, 000, we obtain t ≤ 12, z ≤ 4, x ≤ 8. Notice also that since we have restricted ourselves to even numbers and digits, we have t ∈ {1, 3, 5, 7}. Case 1: z = 4. Since 74 = 2401, then x ≥ 2, but 2401 · 9 > 10, 000, which exceeds the bound – a con ...
... multiple of 5. Thus, y = 0. By the bound xyz(t + 1) ≤ 10, 000, we obtain t ≤ 12, z ≤ 4, x ≤ 8. Notice also that since we have restricted ourselves to even numbers and digits, we have t ∈ {1, 3, 5, 7}. Case 1: z = 4. Since 74 = 2401, then x ≥ 2, but 2401 · 9 > 10, 000, which exceeds the bound – a con ...
2006_30
... and the integer itself resulted in the definition of perfect numbers (A number which is equal to the sum of its proper divisors e.g 6, 28). Thus mathematicians defined an interesting function, an arithmetical function: Sum of proper divisors of an integer. This arithmetical function is related to th ...
... and the integer itself resulted in the definition of perfect numbers (A number which is equal to the sum of its proper divisors e.g 6, 28). Thus mathematicians defined an interesting function, an arithmetical function: Sum of proper divisors of an integer. This arithmetical function is related to th ...
2210 fall 2002 Exponential and log functions Exponential functions
... 2210 fall 2002 Exponential and log functions Exponential functions, even simple ones like 10x, or 2x, are relatively difficult to describe and to calculate because they involve taking high roots of integers, and we do not know much even about computing square roots, much less cube roots or fifth roo ...
... 2210 fall 2002 Exponential and log functions Exponential functions, even simple ones like 10x, or 2x, are relatively difficult to describe and to calculate because they involve taking high roots of integers, and we do not know much even about computing square roots, much less cube roots or fifth roo ...
Chapter 3 Propositions and Functions
... Roughly, two propositions are equal if and only if they are word for word the same. Thus “1 + 1 = 2” and “2 = 1 + 1” are not equal propositions, although they are equivalent. The only time I will use an “=” sign between propositions is in definitions. For example, I might define a proposition form P ...
... Roughly, two propositions are equal if and only if they are word for word the same. Thus “1 + 1 = 2” and “2 = 1 + 1” are not equal propositions, although they are equivalent. The only time I will use an “=” sign between propositions is in definitions. For example, I might define a proposition form P ...
Weekly Homework Sheet
... vote in this year’s election. If 8 people can vote in each voting booth, how many voting booth will the county need? 448 ...
... vote in this year’s election. If 8 people can vote in each voting booth, how many voting booth will the county need? 448 ...
Section 2
... Proof that the Euclidean Algorithm Produces the gcd(a, b) To show that rn , the last non-zero remainder, is, the gcd(a, b) for a b , we must show the following steps: 1. rn | a and rn | b ( rn is a divisor of both a and b). 2. rn is the largest common divisor of a and b. 3. rn will always exist, t ...
... Proof that the Euclidean Algorithm Produces the gcd(a, b) To show that rn , the last non-zero remainder, is, the gcd(a, b) for a b , we must show the following steps: 1. rn | a and rn | b ( rn is a divisor of both a and b). 2. rn is the largest common divisor of a and b. 3. rn will always exist, t ...
Section 2
... Proof that the Euclidean Algorithm Produces the gcd(a, b) To show that rn , the last non-zero remainder, is, the gcd(a, b) for a b , we must show the following steps: 1. rn | a and rn | b ( rn is a divisor of both a and b). 2. rn is the largest common divisor of a and b. 3. rn will always exist, t ...
... Proof that the Euclidean Algorithm Produces the gcd(a, b) To show that rn , the last non-zero remainder, is, the gcd(a, b) for a b , we must show the following steps: 1. rn | a and rn | b ( rn is a divisor of both a and b). 2. rn is the largest common divisor of a and b. 3. rn will always exist, t ...
Chapter 2 - faculty at Chemeketa
... A zero is not significant when it is at the end of a number without a decimal point. 4 Significant Figures ...
... A zero is not significant when it is at the end of a number without a decimal point. 4 Significant Figures ...
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.