(Solution) - Use the Fundamental Theorem of Arithmetic Problem 75 to show -(2025 Original AI-Free Solution)

Paper Details

Use the Fundamental Theorem of Arithmetic (Problem 75) to show that the square of any natural number greater than 1 can be written as the product of primes in a unique way, except for the order of the factors, with each prime occurring an even number of times. For example, (45)2 = 3 ? 3 ? 3 ? 3 ? 5 ? 5.