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1 solution
From the given fact that:
P ( 1 ) = P ( 2 ) = P ( 3 ) = P ( 4 ) = P ( 5 ) = 1
⇒ P ( x ) = A ( x − 1 ) ( x − 2 ) ( x − 3 ) ( x − 4 ) ( x − 5 ) + 1
Therefore,
P ( 2 0 1 4 ) − 1 P ( 2 0 1 5 ) − 1
= A ( 2 0 1 4 − 1 ) ( 2 0 1 4 − 2 ) ( 2 0 1 4 − 3 ) ( 2 0 1 4 − 4 ) ( 2 0 1 4 − 5 ) + 1 − 1 A ( 2 0 1 5 − 1 ) ( 2 0 1 5 − 2 ) ( 2 0 1 5 − 3 ) ( 2 0 1 5 − 4 ) ( 2 0 1 5 − 5 ) + 1 − 1
= A ( 2 0 1 3 ) ( 2 0 1 2 ) ( 2 0 1 1 ) ( 2 0 1 0 ) ( 2 0 0 9 ) A ( 2 0 1 4 ) ( 2 0 1 3 ) ( 2 0 1 2 ) ( 2 0 1 1 ) ( 2 0 1 0 ) = 2 0 0 9 2 0 1 4
⇒ a = 2 0 1 4 , b = 2 0 0 9 and a + b = 2 0 1 4 + 2 0 0 9 = 4 0 2 3