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  3. 2 a 1 point let k n prove that...

Question: 2 a 1 point let k n prove that...

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2. (a) [1 point] Let k, ( N. Prove that 4 14-1. Hint. You can use the identity ak -(a b)(a + a 2abk 2+ bk-1) (b) [3 points] Let m. n e N such that m n. Write m nq + r by the division algorithm, such that 0 Kr <n. Prove that ged(4 1,4 -1)-ged(4 -1,4 -1). Hint. You can use the following fact: for integers a, b, t, such that either aメ0 or b have ged(a, b) -ged(a, b+ ta). (c) [2 points] Using (a) and (b), compute ged(4100-1. 415- 1). 0, we

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