# ws9 - sa tb for some integers s,t(a 21 55(b 123 323 2 mod 7...

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Rob Bayer Math 55 Worksheet July 6, 2009 Instructions Introduce yourselves! Despite popular belief, math is in fact a team sport! Find some blackboard space, a piece of chalk, and decide who will be your ﬁrst scribe. Do the problems below, having a diﬀerent person be the scribe for each one. Try to work out the problems as a group, but feel free to ﬂag me down if you run into a wall. The Euclidean Algorithm 1. Find the gcd of each of the following pairs of numbers and write it as
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Unformatted text preview: sa + tb for some integers s,t (a) 21, 55 (b) 123, 323 2. Compute 13 53 mod 7. 3. (a) Suppose you 2 containers that are 14 gallons and 25 gallons. Show that given an inﬁnitely large “holding tank” you can measure exactly 1 gallon of water. (b) Prove that you cannot measure 1 gallon using just 12 gallon and 21 gallon containers. 4. Prove that if ac ≡ bc ( mod mc ) then a ≡ b ( mod m )...
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