OCR Further Additional Pure AS 2024 June — Question 6

Exam BoardOCR
ModuleFurther Additional Pure AS (Further Additional Pure AS)
Year2024
SessionJune
TopicNumber Theory

6 For positive integers \(n\), let \(f ( n ) = 1 + 2 ^ { n } + 4 ^ { n }\).
    1. Given that \(n\) is a multiple of 3 , but not of 9 , use the division algorithm to write down the two possible forms that \(n\) can take.
    2. Show that when \(n\) is a multiple of 3 , but not of 9 , \(f ( n )\) is a multiple of 73 .
  1. Determine the value of \(\mathrm { f } ( n )\), modulo 73 , in the case when \(n\) is a multiple of 9 .