# JavaScript: Sum of two square numbers equal to an integer

## JavaScript Math: Exercise-110 with Solution

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

For example a^{2} + b^{2} = c where c is the given integer.

Example: 13 = 2^{2} + 3^{2}

**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.

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