My number theory textbook has the following (paraphrased) exercise:
Goldbach wrote a letter to Euler with the following conjecture: Every integer greater than five can be written as the sum of three primes.
Euler replied this statement was equivalent to: Every even integer greater than or equal to 4 can be written as the sum of two primes.
The exercise is to show these two statements are equivalent, and I'm stuck on this. I don't want a solution but nothing is coming to me, so I was just hoping for a hint.