# [970. Powerful Integers](https://leetcode.com/problems/powerful-integers/)


## 题目

Given two positive integers `x` and `y`, an integer is *powerful* if it is equal to `x^i + y^j` for some integers `i >= 0` and `j >= 0`.

Return a list of all *powerful* integers that have value less than or equal to `bound`.

You may return the answer in any order. In your answer, each value should occur at most once.

**Example 1:**

    Input: x = 2, y = 3, bound = 10
    Output: [2,3,4,5,7,9,10]
    Explanation: 
    2 = 2^0 + 3^0
    3 = 2^1 + 3^0
    4 = 2^0 + 3^1
    5 = 2^1 + 3^1
    7 = 2^2 + 3^1
    9 = 2^3 + 3^0
    10 = 2^0 + 3^2

**Example 2:**

    Input: x = 3, y = 5, bound = 15
    Output: [2,4,6,8,10,14]

**Note:**

- `1 <= x <= 100`
- `1 <= y <= 100`
- `0 <= bound <= 10^6`


## 题目大意

给定两个正整数 x 和 y，如果某一整数等于 x^i + y^j，其中整数 i >= 0 且 j >= 0，那么我们认为该整数是一个强整数。返回值小于或等于 bound 的所有强整数组成的列表。你可以按任何顺序返回答案。在你的回答中，每个值最多出现一次。


## 解题思路


- 简答题，题目要求找出满足 `x^i + y^j ≤ bound` 条件的所有解。题目要求输出中不能重复，所以用 map 来去重。剩下的就是 `n^2` 暴力循环枚举所有解。