Parts a through d are connected and all involve the numbers 29 and 8. a) Find...
Parts a through d are connected and all involve the numbers 29 and 8.
a) Find the gcd of 29 and 8 using the Euclidean algorithm. Show each step.
b) Find a solution to 29s + 8t = 1. Remember to use the "backsolving" method and your work in Part a. To start you off, here are the first two steps:
1 = 3 - 2
= 3 - (5 - 3)
c) Let's call your solutions in Part b s0 and t0. Remember, using s0 and t0 we can express all solutions to the original equation, using
s = s0 + _________, and t = t0 - __________. Fill in the blanks with the appropriate expression.
d) Find the biggest negative and smallest positive inverses of 8 (mod 29).
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Parts a through d are connected and all involve the
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