OCR Further Additional Pure AS 2021 November — Question 4

Exam BoardOCR
ModuleFurther Additional Pure AS (Further Additional Pure AS)
Year2021
SessionNovember
TopicNumber Theory
4
  1. Let \(a = 1071\) and \(b = 67\).
    1. Find the unique integers \(q\) and \(r\) such that \(\mathrm { a } = \mathrm { bq } + \mathrm { r }\), where \(q > 0\) and \(0 \leqslant r < b\).
    2. Hence express the answer to (a)(i) in the form of a linear congruence modulo \(b\).
  2. Use the fact that \(358 \times 715 - 239 \times 1071 = 1\) to prove that 715 and 1071 are co-prime.
This paper (8 questions)
View full paper
Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8