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Question: given integers a and b and a gt b if...

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Given integers a and b and a > b if we were to plug them into the Euclidean Algorithm we get: until there is an equation with no remainder left. a. Show that r2 can also be written in the form: r2na+m b, where n and m are integers. Show that for k > 2, if rk-2 and rk-1 can both be written in the form n·a + m . b where n and m are integers, then rk can also be written in the same form. b. Show that the gcd of two numbers a and b can always be written in the formn a+m b where n and m are integers. C.

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