Ta thấy: p,q là 2 số nguyên tố lớn hơn 3\(\Rightarrow p\) \(lẻ\)
\(\Rightarrow p-1;p+1;q-1;q+1⋮2\)
\(Do\) \(p-1;p+1\) \(là\) \(2\) \(số\) \(chẵn\) \(liên\) \(tiếp\)\(\Rightarrow\left(p-1\right)\left(p+1\right)⋮4.2=8\)
\(Tương\) \(tự\) \(với\) \(\left(q-1\right)\left(q+1\right)\Rightarrow\left(q-1\right)\left(q+1\right)⋮8\)
\(\Rightarrow\left(p-1\right)\left(p+1\right)\left(q-1\right)\left(q+1\right)⋮8.8=64\) \(\left(1\right)\)
\(Do\) \(p-1;p;p+1\) \(là\) \(3\) \(số\) \(tự\) \(nhiên\) \(liên\) \(tiếp\) \(nên\) \(chắc\) \(chắn\) \(có\) \(1\) \(số⋮3\) \(mà\) \(p\) \(là\) \(số\) \(nguyên\) \(tố\)
\(\Rightarrow p-1\) \(hoặc\) \(p+1⋮3\)
\(Tương\) \(tự\) \(với\) \(\left(q-1\right)\left(q+1\right)\Rightarrow\left(q-1\right)\left(q+1\right)⋮3\)
\(\Rightarrow\left(p-1\right)\left(p+1\right)\left(q-1\right)\left(q+1\right)⋮3.3=9\) \(\left(2\right)\)
\(Từ\) \(\left(1\right)\) \(và\) \(\left(2\right)\)\(\Rightarrow\left(p-1\right)\left(p+1\right)\left(q-1\right)\left(q+1\right)⋮64.9=576\)
\(\left(đpcm\right)\)
