Check if a number can be expressed as sum of two Perfect powers

Given a positive number N, the task is to check whether the given number N can be expressed in the form of ax + by where x and y > 1 and a and b > 0. If N can be expressed in the given form then print true otherwise print false.

Examples:

Input:_  N = 5_

Output:_ true_

Explanation:

_5 can be expressed as 22+12 _

Input:_ N = 15_

Output:_ false_

Approach: The idea is to use the concept of perfect powers to determine whether the sum exists or not. Below are the steps:

  1. Create an array(say perfectPower[]) to store the numbers which are a perfect power or not.
  2. Now the array perfectPower[] store all the elements which are perfect power, therefore we generate all possible pair sum of all the elements in this array.
  3. Keep the mark of the sum calculated in the above step in an array isSum[] as it can be expressed in the form of ax + by .
  4. After the above steps if isSum[N] is true then print true otherwise print false.

#greedy #mathematical #maths #maths-power #numbers

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Check if a number can be expressed as sum of two Perfect powers
Ray  Patel

Ray Patel

1619607900

Perfect Number Program In Python: How to check if a number is perfect or not?

Introduction

A number is said to be the perfect number if the sum of its proper divisors (not including the number itself) is equal to the number.

To get a better idea let’s consider an example, proper divisors of 6 are 1, 2, 3. Now the sum of these divisors is equal to 6 (1+2+3=6), so 6 is said to be a perfect number. Whereas if we consider another number like 12, proper divisors of 12 are 1, 2, 3, 4, 6. Now the sum of these divisors is not equal to 12, so 12 is not a perfect number.

Programming in Python is relatively simpler and more fun when compared to other languages because of its simpler syntax, good readability. Now that we are clear with the concept of perfect number let’s write a python program to check if a number is a perfect number or not. Let’s build a python code for checking if the given user input is a perfect number or not and explore the fun in coding with python.

#data science #how to check if a number is perfect #perfect number #perfect number in python #perfect number program in python #python

Perfect Number Program In Python: How to check if a number is perfect or not?

Introduction

A number is said to be the perfect number if the sum of its proper divisors (not including the number itself) is equal to the number.

To get a better idea let’s consider an example, proper divisors of 6 are 1, 2, 3. Now the sum of these divisors is equal to 6 (1+2+3=6), so 6 is said to be a perfect number. Whereas if we consider another number like 12, proper divisors of 12 are 1, 2, 3, 4, 6. Now the sum of these divisors is not equal to 12, so 12 is not a perfect number.

Programming in Python is relatively simpler and more fun when compared to other languages because of its simpler syntax, good readability. Now that we are clear with the concept of perfect number let’s write a python program to check if a number is a perfect number or not. Let’s build a python code for checking if the given user input is a perfect number or not and explore the fun in coding with python.

#data science #how to check if a number is perfect #perfect number #perfect number in python #perfect number program in python #python

Check if a number can be expressed as sum of two Perfect powers

Given a positive number N, the task is to check whether the given number N can be expressed in the form of ax + by where x and y > 1 and a and b > 0. If N can be expressed in the given form then print true otherwise print false.

Examples:

Input:_  N = 5_

Output:_ true_

Explanation:

_5 can be expressed as 22+12 _

Input:_ N = 15_

Output:_ false_

Approach: The idea is to use the concept of perfect powers to determine whether the sum exists or not. Below are the steps:

  1. Create an array(say perfectPower[]) to store the numbers which are a perfect power or not.
  2. Now the array perfectPower[] store all the elements which are perfect power, therefore we generate all possible pair sum of all the elements in this array.
  3. Keep the mark of the sum calculated in the above step in an array isSum[] as it can be expressed in the form of ax + by .
  4. After the above steps if isSum[N] is true then print true otherwise print false.

#greedy #mathematical #maths #maths-power #numbers

sophia tondon

sophia tondon

1620885491

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sophia tondon

sophia tondon

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