Let ????, ????, ????, be the sequence defined by the following recurrence relation: ???? = ?? ???? = ?? ? ??????? +?? for ?? ? ?? Prove that ???? = ?? ??+?? ? ?? for any integer ?? ? ??.

Prove that ?? ???? ? ?? is divisible by ?? for any positive integer ??. Recall that an integer ?? is divisible by an integer ?? with ?? ? ?? if and only if there exists an integer ?? such that ?? = ?? ? ??.

4. Let ao, al,a2, be the sequence defined by the following recurrence relation: .a 2 a+1 for 2 1 n+1 2n Recall that an integer y is divisible by an integer x with x # 0 if and only if there exists an integer i such that y-x