Date | May 2012 | Marks available | 3 | Reference code | 12M.3dm.hl.TZ0.5 |
Level | HL only | Paper | Paper 3 Discrete mathematics | Time zone | TZ0 |
Command term | Show that | Question number | 5 | Adapted from | N/A |
Question
Use the result and Fermat’s little theorem to show that .
Find and .
Use the Chinese remainder theorem, or otherwise, to evaluate , noting that .
Markscheme
M1A1
by Fermat’s little theorem A1
AG
[3 marks]
(M1)
A1
A1
[3 marks]
form M1
solve M1A1
A1A1
M1A1
[7 marks]
Examiners report
Many candidates were able to complete part (a) and then went on to part (b). Some candidates raced through part (c). Others, who attempted part (c) using the alternative strategy of repeatedly solving linear congruencies, were sometimes successful.
Many candidates were able to complete part (a) and then went on to part (b). Some candidates raced through part (c). Others, who attempted part (c) using the alternative strategy of repeatedly solving linear congruencies, were sometimes successful.
Many candidates were able to complete part (a) and then went on to part (b). Some candidates raced through part (c). Others, who attempted part (c) using the alternative strategy of repeatedly solving linear congruencies, were sometimes successful.