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I keep getting stuck when I try to prove that the sum of two even numbers is always even. I start by letting the numbers be 2a and 2b, but when I add them to get 2(a+b), I feel like I'm just restating the definition instead of proving why that result must itself be even.

i get the feeling too. the trick for me was not to chase the form but to frame it as a multiple of two. write the numbers as two times a and two times b the sum ends up two times a plus two times b which is two times the sum of a and b and that shows the result is a multiple of two

i tried with real numbers like 4 and 6 the sum is 10 which is divisible by two so it works there too but that feels like a single example not a real proof

maybe the issue isnt the algebra maybe youre asking for a proof that feels formal and you are missing that the definition itself is the key is that right?

one time i drifted to a side thought about parity in coins counting and then came back to the same idea the numbers you wrote still land on a multiple of two and that small moment of wandering helped me keep from overthinking

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