Some Analysis

• In a perfect square, all the factors are raised to an even exponent.
• Thus, when multiplying integers to form a perfect square, what matters is their uneven-exponented factors.
• Thus, an integer can be represented (as far as we're concerned) as a vector of its squaring factors:
• • 120 = 2^3 * 3^1 * 5^1
  • 120[sq] = 2 * 3 * 5
• When multiplying two squaring vectors, their components cancel each other. So if p existed in both vectors, it won't exist in the product.