<s>[INST] If $2^{12} - 1$ is written as a product of powers of primes, the prime factorization of the term $2^{12} - 1$ includes $37$ as a prime factor. This is helpful to determine the decimal representation of the following product and sum with expectation for $0 < x < 1$ and prime number $q$ $$\left((2 + 3)^{(2^{12} - 1)} - 5^{(2^{12} - 1)} \right) = k\cdot q.$$[/INST]