OCR Further Additional Pure AS 2022 June — Question 4

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

4 Let \(\mathrm { N } = 10 \mathrm { a } + \mathrm { b }\) and \(\mathrm { M } = \mathrm { a } + 3 \mathrm {~b}\), where \(a\) and \(b\) are integers such that \(a \geqslant 1\) and \(0 \leqslant b \leqslant 9\).
  1. Prove that \(29 \mid N\) if and only if \(29 \mid M\).
  2. Use an iterative method based on the result of part (a) to show that 899364472 is a multiple of 29 .