number theory problems

The countable numbers are called Natural Numbers. Therefore 1 is the smallest or least of all natural numbers. The highest natural number cannot be said because Natural numbers are infinite. The set of Natural numbers is a subs..

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., ..

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 complex number x + iy is also written as an ordered pair (x, y) and is denoted by z. i.e., z = x + iy The positive value is called the..

The rational numbers can be expressed as terminating or recurring decimals. Decimal fraction has denominator as 10 or a power of 10. A recurring decimal is denoted by placing dots or a bar over recurring digit..

Numbers which are not rational are called irrational numbers. When expressed as decimals, they are non-terminating and non-recurring. i.e., Irrational numbers cannot be put in the form where and are some examples of irrationals. (i) is also irrational. Its approximate ..

Imaginary Number - Square root of a negative number is known as an imaginary number. a > 0 is an imaginary number. or A number whose square is negative is known as an imaginary number. . . . The symbol i, We write, Powers of ..

To mark , an irrational number, on the number line. Let OA = AB = 1 unit and Then in rt. = 1 + 1 Cut off OP = OB = on the number l..

Summary - A rational number is a number of the form where p and q are integers and . Problems involving rational numbers are simplified using 'BODMAS' rule. A rational number can be represented in the decimal form. When a rational number i..

The complex number 0 + i0 is the additive identity for the set of complex numbers. 0 + i0 is called the additive identity for the complex number. Z + (0 + i 0 ) = a + i b + (0 + i 0) = (a + 0) + i (b + 0) = a + i..

The complex number Z = x + iy may be represented graphically by the point P whose rectangular co-ordinates are (x, y). Thus each point in the plane is associated with a complex number..