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UKMT Mathematical Olympiad for Girls, 2018

Number theory Difficulty 3.0 AMC 10/12 Prove it United Kingdom

(a) Write down the full factorisation of the expression $a^2 - b^2$ .
(i) Show that $359999$ is not prime.
(ii) Show that $249919$ is not prime.
Hint: You can use your factorisation of $a^2 - b^2$ if you like.

(b) Write down the full factorisation of $a^2 + 2ab + b^2$ .
(i) Show that $9006001$ is not prime.
(ii) Show that $11449$ is not prime.

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