[Solved]1 Find Integers S T 172s 151t 1 Full Credit Find Smallest Magnitude Integers Hint First F Q37298493

1. Find integers s, t such that 172s + 151t == 1. For fullcredit, find the smallest magnitude integers you can. Hint: Firstfind gcd(151, 172) = 1.

2. (a) In lecture, we saw Euler’s Totient Function Φ(n), whichis defined as the number of positive integers less than or equal ton that are relatively prime to n. Suppose I want to compute Φ(84),as per lecture. I know that 84 = 14 × 6, so I compute Φ(14) andmultiply it by Φ(6). Do I get the right result? Briefly, why doesthis work or not work? Your answer should be brief, but not assimple as “because the numbers do/don’t multiply to form that.” (b)Compute Φ(84). Show your work.

3. Calculate 9200 mod 77. Show your work. For purposes ofshowing your work, do not assume you have access to a programmable(e.g., graphing) calculator or internet for purposes of solvingthis problem. To make this fair to all, we will tell you thecorrect number at the end is 67.

Expert Answer

---

Answer to 1. Find integers s, t such that 172s + 151t == 1. For full credit, find the smallest magnitude integers you can. Hint: F… . . .