number theory problems exam preparation

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 = ..

then show that (A+B)+C = A+(B..

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..

The union of the set of rational numbers and irrational numbers forms the set of real numbers. (i) For every real number, there is a corresponding point on the number line. (ii) For every point on the number line, there exists a real..

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..

Real Numbers - The union of the set of rational numbers and irrational numbers forms the set of real numbers. Q = {rational numbers} = {irrational numbers} Then = R = {real numbers..

It has factors other than one and itself, e.g., 21 is a composite number..