OCR Further Additional Pure 2022 June — Question 2

Exam BoardOCR
ModuleFurther Additional Pure (Further Additional Pure)
Year2022
SessionJune
TopicNumber Theory

2 Consider the integers \(a\) and \(b\), where, for each integer \(n , \mathrm { a } = 7 \mathrm { n } + 4\) and \(\mathrm { b } = 8 \mathrm { n } + 5\). Let \(\mathrm { h } = \mathrm { hcf } ( \mathrm { a } , \mathrm { b } )\).
  1. Determine all possible values of \(h\).
  2. Find all values of \(n\) for which \(a\) and \(b\) are not co-prime.