Hook and content bijections

We provide a bijective proof of the identity ∑ x ∈ λ ( h ( x ) 2 − c ( x ) 2 ) = | λ | 2 where λ is an integer partition, h ( x ) is the hook number of the cell x ∈ λ , and c ( x ) is the content of x . A closely related identity is also proved bijectively.