Problem 3. Consider the Euclidean algorithm to find gcd(a,6), where we set T0, b T1. Let T1, Tn be the sequence of remainders and 41, Jn be the sequence of quotients. Show what you get from the sum Ci_1 Tiqi. Also show what you get from the sum Ci_17qi. (Hint: As always, start with some examples to see what the pattern is. To prove the answer you just need that each step in the Euclidean algorithm was Ti-1 = √(Ti +ri+1))