Question: 1. [6 marks] Number theory. (a) [2 marks ] Prove that nZ,gcd(9n+1,10n+1)=1. HINT: Use some of the facts from the Week 4 worksheets for a

1. [6 marks] Number theory. (a) [2 marks ] Prove that

1. [6 marks] Number theory. (a) [2 marks ] Prove that nZ,gcd(9n+1,10n+1)=1. HINT: Use some of the facts from the Week 4 worksheets for a very short proof. (b) [4 marks ] Prove the following statement: m,nZ,nmPrime(n)n(m+1)

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