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.
107 exam-style questions on Edexcel A Level Maths 1.1 Proof by Contradiction. Each one has a worked solution and a mark scheme showing where the marks go.