SUMMARY
The theorem states that if n² + 1 is odd, then n must be even. An indirect proof involves assuming the opposite, that n is odd, which leads to a contradiction. If n is odd, then n² is also odd, making n² + 1 even, contradicting the original statement. Therefore, the assumption is false, confirming that n must be even when n² + 1 is odd.
PREREQUISITES
- Understanding of even and odd integers
- Familiarity with indirect proof techniques
- Basic knowledge of mathematical logic
- Experience with the properties of numbers
NEXT STEPS
- Study indirect proof methods in mathematical reasoning
- Explore properties of even and odd numbers in depth
- Learn about mathematical contradictions and their role in proofs
- Investigate other theorems involving parity and their proofs
USEFUL FOR
Mathematics students, educators, and anyone interested in formal proof techniques and number theory.