What you're looking for is not called the "characteristics equation", but the characteristic polynomial.
More test cases, please. ;-)
Project Euler: Problem 1, Multiples of 3 and 5
Bottles of beer
CONVERT TAN TO SIN
Returning a "greater than" vector
Fibonacci-Sum of Squares
Convert decimal to hex as shown in test cases
Convert Decimal Number to Hex number (including non integer value)
Try and Catch Simple Example
Flip the vector from right to left
Find out sum and carry of Binary adder
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