Problem 37E

Use Exercise 36 to show that if a and b are positive integers, then gcd(2a- 1, 2b - 1) = 2gcd(a,b)-1. [Hint: Show that the remainders obtained when the Euclidean algorithm is used to compute gcd(2a -1, 2b-1) are of the form 2r - 1. where r is a remainder arising when the Euclidean algorithm is used to find gcd(a, b).]

Week 1 and 2 of College Pre-algebra Life Saver notes! Order of operations Remember GEMDAS 1.G rouping 2.E xponents 3.M ultiply 4.D ivide 5.A dd 6.S ubtract NOTE: when multiplying, dividing, adding, and subtracting you do it as you are reading a book; you go left to right. Important things to remember!: When there are parenthesis ( ) inside of brackets [ ] be sure to do the parenthesis inside of the brackets first. Ex: 35- [3+(9-7)-2] The first step of the problem would be what is in the parenthesis, so (9-7) then you can solve for what remains left in the larger bracket. Don't be intimidated if you see fractions! Fractions just simply mean divide | | aka absolute value is considered a grouping symbol When you have to find