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Question Number 42719 by jbm last updated on 01/Sep/18

Commented by Joel578 last updated on 02/Sep/18

Sophie Germain  p^4  + 4q^4  = (p^2  + 2pq + 2q^2 )(p^2  − 2pq + 2q^2 )                      = ((p + q)^2  + q^2 )((p − q)^2  + q^2 )

$$\mathrm{Sophie}\:\mathrm{Germain} \\ $$$${p}^{\mathrm{4}} \:+\:\mathrm{4}{q}^{\mathrm{4}} \:=\:\left({p}^{\mathrm{2}} \:+\:\mathrm{2}{pq}\:+\:\mathrm{2}{q}^{\mathrm{2}} \right)\left({p}^{\mathrm{2}} \:−\:\mathrm{2}{pq}\:+\:\mathrm{2}{q}^{\mathrm{2}} \right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\left(\left({p}\:+\:{q}\right)^{\mathrm{2}} \:+\:{q}^{\mathrm{2}} \right)\left(\left({p}\:−\:{q}\right)^{\mathrm{2}} \:+\:{q}^{\mathrm{2}} \right) \\ $$

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