Question 1

Paper 1, no calculatorHard6 marks
(a)

Use mathematical induction to prove that 55 divides 2n+3n2^n+3^n for every positive odd integer nn

[4]
(b)

A student conjectures that 2n+3n2^n+3^n is prime for every positive integer nn Use your result from part (a) to disprove this conjecture, explaining why your example is a counterexample.

[2]

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