In the field of cryptography, certain protocols rely on the property that specific constants are not rational. Let S S\,S be a constant defined by the equation S2−13=0S^2 - 13 = 0S2−13=0. Given that S>0S > 0S>0, prove by contradiction that S S\,S is an irrational number.
(You may assume that if n2 n^2\,n2 is a multiple of 13, then n n\,n is also a multiple of 13 for any integer nnn.)
Practise AQA A Level Maths 1.4 A: Proof with exam-style questions for A Level Maths. 107 questions covering 1.4.1 Structure and methods of proof, matched to the AQA A Level Maths (7357) 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.
