Trace Algorithm 4 when it is given m = 5 , n = 11 , and b = 3 as input. That is, show all the steps Algorithm 4 uses to find 3 mod 5 .
The value is .
From the recursive definition,
Evaluate the recursive definition at n = 11 , m = 5 and b = 3.
Determine mpower (3,5,5).
Determine mpower (3,2,5).
Evaluate the found expression for mpower (3,5,5).
Evaluate the found expression for mpower (3,11,5).
Therefore, the value is .
A jigsaw puzzle is put together by successively joining pieces that fit together into blocks. A move is made each time a piece is added to a block, or when two blocks are joined. Use strong induction to prove that no matter how the moves are carries out, exactly n -1 moves are required to assemble a puzzle with n pieces.
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