Problem
NT-B1-M06-P001 Parity of a Square
#1
★☆☆☆☆ Level 1 of 5
Prove that if \(a^2\) is divisible by \(2\), then \(a\) is divisible by \(2\).
Argue by contradiction: the square of an odd integer is odd.
If \(a\) is odd, then \(a=2k+1\). Then \(a^2=4k^2+4k+1\), which is odd. Hence if \(a^2\) is even, \(a\) cannot be odd, so \(a\) is even.
Basic fact for all later parity descents.