IOSR Journal of Mathematics (IOSR-JM) e-ISSN: 2278-5728,p-ISSN: 2319-765X,
... Here a new conjecture about the prime numbers can be introduced to deduce the reality of Goldback’s puzzle about natural numbers. The new conjecture is “there is at least a prime-prime distribution at a same distance in both sides from a number of natural numbers series except 1, 2 and 3”. The conte ...
... Here a new conjecture about the prime numbers can be introduced to deduce the reality of Goldback’s puzzle about natural numbers. The new conjecture is “there is at least a prime-prime distribution at a same distance in both sides from a number of natural numbers series except 1, 2 and 3”. The conte ...
Methods of Proofs Predicate Logic Odd and Even Numbers
... Example: u If we have 1 computer for all students, we say: t ∃ one computer ∀ students u If each student has a separate computer t ∀ students ∃ one computer ...
... Example: u If we have 1 computer for all students, we say: t ∃ one computer ∀ students u If each student has a separate computer t ∀ students ∃ one computer ...
4.6.36 Rational Inequality
... The third step is to factor the rational expression on the left, and it is. Then the numbers that make the rational expression zero are x = 3 and x = −2, and the number that makes the expression undefined is x = 1. We put these on a number line, and then test the value of the rational expression for ...
... The third step is to factor the rational expression on the left, and it is. Then the numbers that make the rational expression zero are x = 3 and x = −2, and the number that makes the expression undefined is x = 1. We put these on a number line, and then test the value of the rational expression for ...
Multiplication and Division of Whole Numbers
... Notice that both the divisor and the quotient are factors of the dividend. To find the factors of a number, try dividing the number by 1, 2, 3, 4, 5, … Those numbers that divide into the number evenly are its factors. Continue this process until the factors start to repeat. A prime number is a natur ...
... Notice that both the divisor and the quotient are factors of the dividend. To find the factors of a number, try dividing the number by 1, 2, 3, 4, 5, … Those numbers that divide into the number evenly are its factors. Continue this process until the factors start to repeat. A prime number is a natur ...
Properties of Whole Numbers (PDF 108KB)
... A whole number greater than 1 that has only two factors, 1 and itself, is known as a Prime Number. What does this mean? For example: The factors of 2 are only 2 & 1; itself and 1, hence 2 is a Prime Number What about 5? The only factors of 5 are itself and 1, so yes it is. Ok how about 6? NO, why? B ...
... A whole number greater than 1 that has only two factors, 1 and itself, is known as a Prime Number. What does this mean? For example: The factors of 2 are only 2 & 1; itself and 1, hence 2 is a Prime Number What about 5? The only factors of 5 are itself and 1, so yes it is. Ok how about 6? NO, why? B ...
Divisibility fact: An integer is divisible by 9 if the su is divisible by 9.
... Problem of the Week Problem C Palindrome Hunt A palindrome is a word, phrase, number, or other sequence of characters which reads the same backward or forward. The number 9876789 is a seven-digit palindrome. Find all seven-digit palindromes that satisfy each of the following conditions: • four of th ...
... Problem of the Week Problem C Palindrome Hunt A palindrome is a word, phrase, number, or other sequence of characters which reads the same backward or forward. The number 9876789 is a seven-digit palindrome. Find all seven-digit palindromes that satisfy each of the following conditions: • four of th ...
Place Value and Names for Numbers ADA
... The Hindu-Arabic numerals 0 1 2 3 4 5 6 7 8 9 are called digits. We can form any number in the number system by selecting one or more digits and placing them in certain positions. Each position has a particular value. The Hindu mathematician who devised the system in about 500 A.D. stated that from ...
... The Hindu-Arabic numerals 0 1 2 3 4 5 6 7 8 9 are called digits. We can form any number in the number system by selecting one or more digits and placing them in certain positions. Each position has a particular value. The Hindu mathematician who devised the system in about 500 A.D. stated that from ...
FACTORS AND MULTIPLES theory explained - pita
... and 2) listing each of those divisors on the left with its corresponding factor on the right until 3) eventually we reach the halfway mark of the number and know that we have them all We are finding a quick, orderly method of listing all the factors. When the number is a perfect square and has a fac ...
... and 2) listing each of those divisors on the left with its corresponding factor on the right until 3) eventually we reach the halfway mark of the number and know that we have them all We are finding a quick, orderly method of listing all the factors. When the number is a perfect square and has a fac ...
Non Calculator Arithmetic
... f) If we try to move the decimal point three places to the right, we seem to ‘run out’, as multiplying 1.95 by 100 gives us 195, which is a whole number. We still have to multiply by another 10, so we must use the ‘whole number’ method and insert an extra 0 on the end, so 1.95 1000 = 1950. g) We c ...
... f) If we try to move the decimal point three places to the right, we seem to ‘run out’, as multiplying 1.95 by 100 gives us 195, which is a whole number. We still have to multiply by another 10, so we must use the ‘whole number’ method and insert an extra 0 on the end, so 1.95 1000 = 1950. g) We c ...
Some Simple Number Problems
... 2. Show that a whole number is divisible by 9 if its digits add up to a multiple of 9. So, for example 972 is divisible by 9 as 9 7 2 18 , which is a multiple of 9.2. 3. Show that a whole number is divisible by 4 if its last two digits are divisible by 4.3 4. Prove that the sum of two odd numb ...
... 2. Show that a whole number is divisible by 9 if its digits add up to a multiple of 9. So, for example 972 is divisible by 9 as 9 7 2 18 , which is a multiple of 9.2. 3. Show that a whole number is divisible by 4 if its last two digits are divisible by 4.3 4. Prove that the sum of two odd numb ...
Square Numbers
... polygonal number, completing the larger polygon, and placing vertexes and other points where necessary. The third polygonal number is found by adding all the vertexes and points in the resulting figure. (Look at the table below for a clearer explaination). My colleagues' formula (the Shi-Cheng form ...
... polygonal number, completing the larger polygon, and placing vertexes and other points where necessary. The third polygonal number is found by adding all the vertexes and points in the resulting figure. (Look at the table below for a clearer explaination). My colleagues' formula (the Shi-Cheng form ...
PRIME MATHgazine Junior
... 2) If today is Wednesday October 9th, what is the day that is 1 week before 2 days after yesterday? ___________ Day of the week ...
... 2) If today is Wednesday October 9th, what is the day that is 1 week before 2 days after yesterday? ___________ Day of the week ...
Sum of cubes of the first "n" natural numbers
... of the first n natural numbers, using the manipulation of a three-dimensional geometric model. Introduction In the number theory, the sum of the first n cubes is given by the square of the n-th triangular number, that is, ...
... of the first n natural numbers, using the manipulation of a three-dimensional geometric model. Introduction In the number theory, the sum of the first n cubes is given by the square of the n-th triangular number, that is, ...
Lesson 89: Solving Problems with Two Unknowns by Graphing
... Notice we are given two pieces of information about two numbers. One piece of information is that their sum is 6. we can write that information as an equation. We will use x and y to represent the two numbers. ...
... Notice we are given two pieces of information about two numbers. One piece of information is that their sum is 6. we can write that information as an equation. We will use x and y to represent the two numbers. ...
Arithmetic Sequences and Geometric Sequences
... each of the terms in a series. • For example: 1, 5, 9, 13… The common difference (d) is +4. • The d term can also be negative: 10, 7, 4, 1, -2… The d term is -3 (this means that instead of adding a number you subtract it.) ...
... each of the terms in a series. • For example: 1, 5, 9, 13… The common difference (d) is +4. • The d term can also be negative: 10, 7, 4, 1, -2… The d term is -3 (this means that instead of adding a number you subtract it.) ...
Name : Teacher : Date : Score :
... 3 ) The sum of two numbers times a third number is equal to the sum of each addend times the third number. For example a x (b + c) = a x b + a x c ...
... 3 ) The sum of two numbers times a third number is equal to the sum of each addend times the third number. For example a x (b + c) = a x b + a x c ...
Worksheet Number Fifteen Amicable Numbers and Thabit ibn Qurra
... in this course. The last theorem in book IX of Euclid, Theorem IX.36 states that if 2 n +1 "1 is a prime number then 2 n " (2 n +1 #1) is a perfect number. Examples are 6, 28, 496 and 8,128. This is the pinnacle of ancient Greek number theory. The only amicable numbers known to the ancient Greeks we ...
... in this course. The last theorem in book IX of Euclid, Theorem IX.36 states that if 2 n +1 "1 is a prime number then 2 n " (2 n +1 #1) is a perfect number. Examples are 6, 28, 496 and 8,128. This is the pinnacle of ancient Greek number theory. The only amicable numbers known to the ancient Greeks we ...
Module 3 Notes Prime numbers: -Prime numbers have exactly two
... -If you are an integer you are also a rational number but you may not be a whole number nor a natural number. Ordering Real Numbers -Real numbers can be plotted as points on a number line. A number line is a visual representation of real numbers. The numbers on the number line increase from left to ...
... -If you are an integer you are also a rational number but you may not be a whole number nor a natural number. Ordering Real Numbers -Real numbers can be plotted as points on a number line. A number line is a visual representation of real numbers. The numbers on the number line increase from left to ...
Full text
... there are, and it is this observation we use to calculate an. Trivially, the only two-digit code is 10 and the only three-digit code is 110. There are precisely three four-digit codes—1010, 1100, 1110—and three five-digit codes—10010, 11100, 11110. Thus, ax=a2=l and a3 = a4 = 3. It should be noted t ...
... there are, and it is this observation we use to calculate an. Trivially, the only two-digit code is 10 and the only three-digit code is 110. There are precisely three four-digit codes—1010, 1100, 1110—and three five-digit codes—10010, 11100, 11110. Thus, ax=a2=l and a3 = a4 = 3. It should be noted t ...
Mathemagic 4
... Digital root of the integer n is calculated by adding up all its digits to obtain the first digital sum. If this sum is 10 or greater then repeat the same process for it to obtain the second digital sum. Continue until the sum is less than 10. This final sum is the digital root of the original numbe ...
... Digital root of the integer n is calculated by adding up all its digits to obtain the first digital sum. If this sum is 10 or greater then repeat the same process for it to obtain the second digital sum. Continue until the sum is less than 10. This final sum is the digital root of the original numbe ...
Notes
... Example 2. Find the number of 8 digit numbers formed only using the digits 4, 5, 6 which are (a) even (b) divisible by 5 (c) divisible by 3. (a) For such a number to be even, the units digit has to be even, hence 4 or 6. Thus there are two choices for the units digit, and 3 choices for each of the r ...
... Example 2. Find the number of 8 digit numbers formed only using the digits 4, 5, 6 which are (a) even (b) divisible by 5 (c) divisible by 3. (a) For such a number to be even, the units digit has to be even, hence 4 or 6. Thus there are two choices for the units digit, and 3 choices for each of the r ...
DIVISIBILITY BY (10N-1)
... that is k-1 digits or will reduce to one that is. Thus we will show it true for those which have f1f2...fk which are (10N-1) times a nuber with k-1 digits, then by the fact that the other numbers with k+1 digits reduce to these we can use an identical process on those. Thus by the induction step (B) ...
... that is k-1 digits or will reduce to one that is. Thus we will show it true for those which have f1f2...fk which are (10N-1) times a nuber with k-1 digits, then by the fact that the other numbers with k+1 digits reduce to these we can use an identical process on those. Thus by the induction step (B) ...
2004 Questions
... round. The minimum number of points, which will guarantee advancement without getting involved in any tiebreakers, is (a) 3 ...
... round. The minimum number of points, which will guarantee advancement without getting involved in any tiebreakers, is (a) 3 ...