Integer polynomial
Introduction :
In mathematics, an integer polynomial P(t) is a polynomial taking an integer value P(n) for every integer n. Certainly every polynomial with integer coefficients is integer-valued. There are simple examples to show that the converse is not true: example of polynomial
` (t (t+1))/(2)`
giving the triangle numbers takes on integer values whenever t = n is an integer. That is because one out of n and n + 1 must be an even number.
Pk(t) = t(t − 1)...(t − k + 1)/k! for k = 0,1,2, ... . (Source: Wikipedia)
Explanation of integer polynomials:
In the integer polynomial express the values of all the real numbers. In the every polynomial are the integer coefficients.
Here will explain the integer polynomials in the example
Integer even numbers can be expressed by using the following general formula of integer polynomials,
` (t(t+1))/(2)`
This formula using to evaluate the real number.
For example t=5 we take to express the equation Answer for this problem. We will substitute the value in above formula,
If t=n is an integer, then the integer polynomial values in the triangle number is given by,
n (n+1)/2 must be the even number.
= 5(5+1)/2
=5(6)/2
=30/2
Answer = 15
Examples of integer polynomial:
Example1:
To find the value of the given problem ? If t=10 and find the polynomial
Solution:
We use the formula and express the given problem
Formula =`(t(t+1))/(2)`
=`(10*(10+1))/(2)`
=`(10*11)/(2)`
=`(110)/(2)`
Answer =55
In each of the polynomial with the numerical coefficient of integer.
Example2:
To find the value of the given problem? If t=9 and find the polynomial
Solution:
We use the formula and express the given problem
Formula=`(t(t+1))/2`
=`(9*(9+1))/(2)`
=`(9*10)/(2)`
= `(90)/(2)`
Answer = 45
In each of the polynomial with the numerical coefficient of integer.
In mathematics, an integer polynomial P(t) is a polynomial taking an integer value P(n) for every integer n. Certainly every polynomial with integer coefficients is integer-valued. There are simple examples to show that the converse is not true: example of polynomial
` (t (t+1))/(2)`
giving the triangle numbers takes on integer values whenever t = n is an integer. That is because one out of n and n + 1 must be an even number.
Pk(t) = t(t − 1)...(t − k + 1)/k! for k = 0,1,2, ... . (Source: Wikipedia)
Explanation of integer polynomials:
In the integer polynomial express the values of all the real numbers. In the every polynomial are the integer coefficients.
Here will explain the integer polynomials in the example
Integer even numbers can be expressed by using the following general formula of integer polynomials,
` (t(t+1))/(2)`
This formula using to evaluate the real number.
For example t=5 we take to express the equation Answer for this problem. We will substitute the value in above formula,
If t=n is an integer, then the integer polynomial values in the triangle number is given by,
n (n+1)/2 must be the even number.
= 5(5+1)/2
=5(6)/2
=30/2
Answer = 15
Examples of integer polynomial:
Example1:
To find the value of the given problem ? If t=10 and find the polynomial
Solution:
We use the formula and express the given problem
Formula =`(t(t+1))/(2)`
=`(10*(10+1))/(2)`
=`(10*11)/(2)`
=`(110)/(2)`
Answer =55
In each of the polynomial with the numerical coefficient of integer.
Example2:
To find the value of the given problem? If t=9 and find the polynomial
Solution:
We use the formula and express the given problem
Formula=`(t(t+1))/2`
=`(9*(9+1))/(2)`
=`(9*10)/(2)`
= `(90)/(2)`
Answer = 45
In each of the polynomial with the numerical coefficient of integer.