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Pearson Edexcel Level 3 GCE., Further Mathematics Advanced PAPER 4A: Further Pure Mathematics 2

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1. In this question you must show detailed reasoning. Without performing any division, explain why n = 20 210520 is divisible by 66 2. A binary operation  on the set of non‑negative integers, � ... ��+0, is defined by m  n = ½m – n½ m, n ∈ +0 (a) Explain why +0 is closed under the operation  (1) (b) Show that 0 is an identity for (+0, ) (2) (c) Show that all elements of +0 have an inverse under  (2) (d) Determine if +0 forms a group under , giving clear justification for your answer. (3 3. (a) Use the Euclidean Algorithm to find integers a and b such that 125a + 87b = 1 (5) (b) Hence write down a multiplicative inverse of 87 modulo 125 (1) (c) Solve the linear congruence 87x ≡ 16 (mod 125) [Show More]

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