A bijective proof is given for the following theorem: The number of compositions of n into parts congruent to a (mod b) equals the number of compositions of n + b - a into parts congruent to b (mod a) that are greater than or equal to b. The bijection is then shown to preserve palindromicity.
Diffenderfer, James D..
"Building a Better Bijection between Classes of Compositions."
Integers, 14: A44.