OCR
Further Additional Pure AS
2021
November
— Question 7
Exam Board
OCR
Module
Further Additional Pure AS (Further Additional Pure AS)
Year
2021
Session
November
Topic
Number Theory
7
Let \(f ( n ) = 2 ^ { 4 n + 3 } + 3 ^ { 3 n + 1 }\).
Use arithmetic modulo 11 to prove that \(\mathrm { f } ( n ) \equiv 0 ( \bmod 11 )\) for all integers \(n \geqslant 0\).
Use the standard test for divisibility by 11 to prove the following statements.