In a specific cryptographic protocol, a validation factor VVV is calculated for prime numbers ppp using the formula V(p)=p2−1V(p) = p^2 - 1V(p)=p2−1 Prove that for every prime number ppp in the range 10<p<2010 < p < 2010<p<20, the validation factor V(p)V(p)V(p) is a multiple of 24.
A software engineer claims that for any non-negative integer nnn, the processing time T(n)=n2+3n+5T(n) = n^2 + 3n + 5T(n)=n2+3n+5 microseconds is never a multiple of 2. Use proof by contradiction to show that this claim is correct.
Practise Edexcel A Level Maths 1.1 Proof by Contradiction with exam-style questions for A Level Maths. 100 questions, 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.