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id	title	challengeType	forumTopicId	dashedName
5a23c84252665b21eecc7eca	Kaprekar numbers	5	302296	kaprekar-numbers

--description--

A positive integer is a [Kaprekar number](https://en.wikipedia.org/wiki/Kaprekar number) if:

It is 1, or,
The decimal representation of its square may be split once into two parts consisting of positive integers which sum to the original number.

Note that a split resulting in a part consisting purely of 0s is not valid, as 0 is not considered positive.Example

Kaprekar numbers:

2223 is a Kaprekar number, as 2223 * 2223 = 4941729, 4941729 may be split to 494 and 1729, and 494 + 1729 = 2223
The series of Kaprekar numbers is known as A006886, and begins as 1, 9, 45, 55, ...

--instructions--

Write a function that takes a number n, a base bs, and returns true if the number is a Kaprekar number for the given base. Otherwise, the function returns false.

--hints--

isKaprekar should be a function.

assert(typeof isKaprekar == 'function');

isKaprekar(1, 10) should return a boolean.

assert(typeof isKaprekar(1, 10) == 'boolean');

isKaprekar(1, 10) should return true.

assert.equal(isKaprekar(1, 10), true);

isKaprekar(9, 10) should return true.

assert.equal(isKaprekar(9, 10), true);

isKaprekar(2223, 10) should return true.

assert.equal(isKaprekar(2223, 10), true);

isKaprekar(22823, 10) should return false.

assert.equal(isKaprekar(22823, 10), false);

isKaprekar(9, 17) should return false.

assert.equal(isKaprekar(9, 17), false);

isKaprekar(225, 17) should return true.

assert.equal(isKaprekar(225, 17), true);

isKaprekar(999, 17) should return false.

assert.equal(isKaprekar(999, 17), false);

--seed--

--seed-contents--

function isKaprekar(n, bs) {

}

--solutions--

function isKaprekar(n, bs) {
  if (n < 1) return false;
  if (n == 1) return true;
  for (var a = n * n, b = 0, s = 1; a; s *= bs) {
    b += (a % bs) * s;
    a = Math.floor(a / bs);
    if (b && a + b == n) return true;
  }
  return false;
}

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