We want to send messages consisting of three integers in seq

We want to send messages consisting of three integers in sequence, allowing for the possibility of an error in the transmission or translation of the message. To do this we find a polynomial of degree at most 2, say f(x), such that f(1), f(2) and f(3) are the three integers, and then transmit f(1), f(2), f(3), f(4), f(5). This should enable us to detect and correct a single error. Supposed the message as translated is 1, 5, 10, 19, 29. Find and correct the error.

Solution

If the message is translated then the original message would be 1,5,10

and the error 19,29