A clean argument, line by line
If n is even, then n² is even.
- 01
Assume n is even.
Assumption - 02
Then n = 2k for some integer k.
Definition - 03
Squaring gives n² = 4k².
Algebra - 04
So n² = 2(2k²), which is even.
Rewrite - 05
Therefore n² is even.
Conclusion
