A security researcher is investigating a cryptographic protocol where valid key pairs (n,m)(n, m)(n,m) must satisfy the property that nnn and mmm are integers such that:
n2−20m−14=0 n^2 - 20m - 14 = 0 n2−20m−14=0Prove that nnn is even.
Hence, prove that 10m+710m + 710m+7 is even and explain why this leads to a contradiction.
Explain what can be deduced about the existence of valid key pairs (n,m)(n, m)(n,m) for this protocol.
Practise Edexcel A Level Maths Algebraic Methods with exam-style questions for A Level Maths. 226 questions covering 1.1 Proof by Contradiction, 1.2 Algebraic Fractions, 1.3 Partial Fractions, 1.4 Repeated Factors, and 1.5 Algebraic Division, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
