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Solve in integers :
(1) 2n = a! + b! + c! ;
(2) a! b! = a! + b! + c! ;
(3) abc + ab + bc + ca + a + b + c = 1000 ;
(4) 2a + 3b = c2 ;
(5) a2 + b2 = abc - 1 ;
(6) y2 = x5 - 4 ;
(7) m2 = n(n + p) where p is an odd prime ;
(8) 49 + 20(61/3) = (m1/3 + n1/3 - 1)2 ;
(9) x2 + 4y = s2, y2 + 4x = t2.
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