Finding a number, when multiplied with input number yields input number in JavaScript

We need to write a JavaScript function that takes a positive integer n and a positive integer p, then finds a value k such that the sum of digits raised to successive powers equals k * n.

Problem Statement

Given a number n with digits a, b, c, d... and a power p, we want to find integer k where:

(a^p + b^(p+1) + c^(p+2) + d^(p+3) + ...) = n * k

If such k exists, return k; otherwise return -1.

Example Walkthrough

For number 695 and p = 2:

• 6^2 + 9^3 + 5^4 = 36 + 729 + 625 = 1390
• Check if 1390 / 695 is an integer: 1390 / 695 = 2
• Since 2 is an integer, k = 2

Solution

const num = 695;
const p = 2;

const findDesiredNumber = (num, p) => {
    let sum = 0;
    let str = String(num);
    let power = p;
    
    // Calculate sum of digits raised to successive powers
    for(let i = 0; i < str.length; i++){
        const digit = parseInt(str[i]);
        sum += Math.pow(digit, power);
        power++;
    }
    
    // Check if sum/num is an integer
    return Number.isInteger(sum / num) ? sum / num : -1;
};

console.log(`Number: ${num}, Power: ${p}`);
console.log(`Result: ${findDesiredNumber(num, p)}`);

Number: 695, Power: 2
Result: 2

Testing with Different Values

const findDesiredNumber = (num, p) => {
    let sum = 0;
    let str = String(num);
    let power = p;
    
    for(let i = 0; i < str.length; i++){
        const digit = parseInt(str[i]);
        sum += Math.pow(digit, power);
        power++;
    }
    
    return Number.isInteger(sum / num) ? sum / num : -1;
};

// Test cases
console.log("Testing 46 with p=1:", findDesiredNumber(46, 1));  // 4^1 + 6^2 = 40, 40/46 ? 0.87
console.log("Testing 89 with p=1:", findDesiredNumber(89, 1));  // 8^1 + 9^2 = 89, 89/89 = 1
console.log("Testing 695 with p=2:", findDesiredNumber(695, 2)); // 6^2 + 9^3 + 5^4 = 1390, 1390/695 = 2

Testing 46 with p=1: -1
Testing 89 with p=1: 1
Testing 89 with p=2: 1
Testing 695 with p=2: 2

How It Works

The algorithm converts the number to a string to access individual digits, then:

1. Iterates through each digit
2. Raises each digit to successive powers starting from p
3. Sums all the powered values
4. Checks if sum/n produces an integer result

Conclusion

This function efficiently finds the multiplier k by calculating the sum of digits raised to successive powers and checking divisibility. It returns the integer quotient if valid, otherwise -1.