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Q.E.D. ~Shomei Shuryo~ is a detective fiction manga by Motohiro Katou. The main character Sou Touma encounters a variety of crimes ranging from murder to fraud. Sou often works in tandem with his friend and potential love interest Kana, with him supplying the brain while she acts as brawn.
The manga is structured similarly to Detective Conan and Kidaichi Shōnen no Jikenbo, where time flows forward for the characters, (in book 3, Sou gives Kana a pearl necklace as a Christmas present. In book 9, the pair are invited to take part in a mystery game during Christmas) yet the background setting is stuck in time. (ie, Sou and Kana are still in the same grades)
The title comes from the Latin quod erat demonstrandum. Sou will typically write the term down when he has solved the case just prior to his explanation. [From Wikipedia]