[Bitwise Power] Quadruple Power Check - Coding Problem

Given an integer n, determine whether it represents a perfect quadruple power—that is, whether n can be expressed as 4 raised to some non-negative integer exponent.

Formally, return true if there exists an integer k where k ≥ 0 such that n = 4^k. Otherwise, return false.

A quadruple power is defined as any value in the sequence: 1, 4, 16, 64, 256, 1024, ... where each subsequent value is obtained by multiplying the previous value by 4.

Your task is to design an efficient algorithm that determines membership in this specific numerical sequence.

16 can be expressed as 4² (4 raised to the power of 2), which equals 16. Therefore, 16 is a valid quadruple power.

5 cannot be expressed as 4 raised to any non-negative integer power. The quadruple powers near 5 are 4¹ = 4 and 4² = 16, and 5 does not equal either.

1 can be expressed as 4⁰ (4 raised to the power of 0), which equals 1. By definition, any positive number raised to the power of 0 equals 1.