Problem
NT-B1-M12-P003 Set 1. Common Divisor
#3
★☆☆☆☆ Level 1 of 5
Prove that any two consecutive odd numbers are coprime or have GCD \(2\)? Correct the statement and prove the true version.
Two odd numbers cannot be consecutive integers; likely the intended numbers differ by \(2\).
Correct statement: two odd numbers differing by \(2\) are coprime. Let the numbers be \(n\) and \(n+2\), with \(n\) odd. Their common divisor divides \(2\). Since both numbers are odd, the common divisor is not divisible by \(2\). Hence the GCD is \(1\).
Training problem on reading the statement.