My domain i numbers of form 4k+1. n divides m is this domain if n=mk for some k in the domain. A number is prime in this domain if its only divisors are 1 and itself. My problem is to find a number in the domain with multiple prime factorizations.
The Attempt at a Solution
If have started by identifying ja series of primes in the domain: 5,9,13,17,21,29, and all other numbers that are prime in our domain and are in this domain (I'll call it M-space). So far I have simply been trying to multiply together randomly and hope to get the same number. I have been unsuccessful. Is there any systematic approach that I could try?