OCR
Further Additional Pure
2021
November
— Question 8
Exam Board
OCR
Module
Further Additional Pure (Further Additional Pure)
Year
2021
Session
November
Topic
Number Theory
8
Solve the second-order recurrence system \(\mathrm { H } _ { \mathrm { n } + 2 } = 5 \mathrm { H } _ { \mathrm { n } + 1 } - 4 \mathrm { H } _ { \mathrm { n } }\) with \(H _ { 0 } = 3 , H _ { 1 } = 7\) for \(n \geqslant 0\).
Write down the quadratic residues modulo 10 .
By considering the sequence \(\left\{ \mathrm { H } _ { \mathrm { n } } \right\}\) modulo 10, prove that \(\mathrm { H } _ { \mathrm { n } }\) is never a perfect square.