JavaScript: Sum of two square numbers equal to an integer

JavaScript Math: Exercise-110 with Solution

Sum of Two Squares Equals Integer

Write a JavaScript program to check whether the sum of two square integers is equal to another given integer.

For example a² + b² = c where c is the given integer.
Example: 13 = 2² + 3²

Test Data:
(2) -> true
(5) -> true
(13) -> true
(15) -> false

Sample Solution:

Solution-1

JavaScript Code:

/**
 * Function to check if a given integer can be represented as the sum of two squares.
 * @param {number} n - The integer to check.
 * @returns {boolean} - True if the integer can be represented as the sum of two squares, otherwise false.
 */
function test(n) {
   // If n is less than or equal to 1, it cannot be represented as the sum of two squares
   if (n <= 1) return false;
   // Calculate the maximum value of the first square (integer part of square root of n - 1)
    max_val = Math.floor(Math.sqrt(n - 1));
    // Iterate from max_val down to 0
    while (max_val >= 0) {
       // Calculate the square root of (n - max_val^2)
       temp = Math.sqrt(n - max_val * max_val);
        // If temp is an integer (no remainder when divided by 1), return true
        if (!(temp % 1)) {
            return true;
        };
        // Decrement max_val for the next iteration
        max_val -= 1;
    };
    // If no valid combination is found, return false
    return false;
}

// Test cases
n = 2;
console.log("n = " + n);
console.log("Check if the sum of two square integers is equal to the said integer: " + test(n));
n = 5;
console.log("n = " + n);
console.log("Check if the sum of two square integers is equal to the said integer: " + test(n));
n = 13;
console.log("n = " + n);
console.log("Check if the sum of two square integers is equal to the said integer: " + test(n));
n = 15;
console.log("n = " + n);
console.log("Check if the sum of two square integers is equal to the said integer: " + test(n));

Output:

n = 2
Check sum of two square integers is equal to said integer: true
n = 5
Check sum of two square integers is equal to said integer: true
n = 13
Check sum of two square integers is equal to said integer: true
n = 15
Check sum of two square integers is equal to said integer: false

Flowchart:

Live Demo:

See the Pen javascript-math-exercise-110 by w3resource (@w3resource) on CodePen.

Solution-2

JavaScript Code:

/**
 * Function to check if a given integer can be represented as the sum of two square integers.
 * @param {number} n - The integer to check.
 * @returns {boolean} - True if the integer can be represented as the sum of two square integers, otherwise false.
 */
function test(n) {
    // If n is less than or equal to 1, it cannot be represented as the sum of two square integers
    if (n <= 1) return false;
    // Iterate over i and j from 0 to the square root of n
    for(var i = 0; i * i <= n; i++){
        for(var j = 0; j * j <= n; j++) {
            // Calculate the squares of i and j
            var a = i * i;
            var b = j * j;
            // If the sum of squares is equal to n, return true
            if (a + b == n)
                return true;
        }
    }    
    // If no valid combination is found, return false
    return false;
}

// Test cases
n = 2;
console.log("n = " + n);
console.log("Check if the sum of two square integers is equal to the said integer: " + test(n));
n = 5;
console.log("n = " + n);
console.log("Check if the sum of two square integers is equal to the said integer: " + test(n));
n = 13;
console.log("n = " + n);
console.log("Check if the sum of two square integers is equal to the said integer: " + test(n));
n = 15;
console.log("n = " + n);
console.log("Check if the sum of two square integers is equal to the said integer: " + test(n));

Output:

n = 2
Check sum of two square integers is equal to said integer: true
n = 5
Check sum of two square integers is equal to said integer: true
n = 13
Check sum of two square integers is equal to said integer: true
n = 15
Check sum of two square integers is equal to said integer: false

Flowchart:

Live Demo:

See the Pen javascript-math-exercise-110-1 by w3resource (@w3resource) on CodePen.

For more Practice: Solve these Related Problems:

• Write a JavaScript function that checks if a given integer can be represented as the sum of two square numbers.
• Write a JavaScript function that iterates through possible square numbers and tests if any two add up to the given integer.
• Write a JavaScript function that uses nested loops to examine combinations of squares up to the square root of the integer.
• Write a JavaScript function that validates the input and returns a boolean indicating if the sum of two squares equals the integer.

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