number theory i

Scientific Notation - Notation of large number in terms of exponential form, 10 raised to required value. It is also a standart notation representation as " p x 10 q ". where 'p' and 'q' are any integer..

Question 1 - Question: Show that the sum of the cubes of any number of consecutive integers is divisible by the sum of those integers. Answer: Let the consecutive integers be (n + 1), (n + 2), (n + 3),....,(n + m) Sum of the cubes of integers = S 1 (n+m) and (n+m+1) are consecutive intege..

Question 1 - Question: For the given sequence, suggest possible next three terms and find the general term. 7, 11, 15,---- Answer: First term = 7, Common Difference = 11 - 7 = 15 - 11 = 4 Next three terms are 15 + 4 = 19, 19 + 4 = 23, 23 + 4 = ..

Square root of a negative number is known as an imaginary number . If x and y are real numbers, then x + iy is called a complex number . x is called the real part and y is called the imaginary part . The following are the types of compl..

A prime number is one that has only two factors namely 1 and itself. and a composite number has factors besides 1 and itsel..

The set of whole numbers is the set of natural numbers along with zero. so W = the set of whole numbers = 0,1,2,3,............ so Zero is the least number of the set of Whole numbers. As the whole numbers is an infinite set we cant d..

Numbers which are not rational are called irrational numbers. When expressed as decimals, they are non-terminating and non-recurring. We can obtain infinite number of irrationals between two irrational numbers..

It can only be divided by one or itself i.e., a prime number has no factors other than 1 and itself. e.g., 2, 3, 5, 7, 11, 13, 17, 19, 23, are examples of prime numbers..

Such numbers have only 1 as common factor even though they may be composite numbers e.g., 21 and 32 are prime to each other. We generally write (21, 32) = 1, which means 21 and 32 are prime to each other i.e., they have only one factor in common viz., ..

We have defined rational numbers as those which can be expressed as fractions: We now define decimal fractions. The rational numbers can be expressed as terminating or recurring decimals. Decimal fraction has denominator as 10 or a power of ..