Coursework.Info - Inspiration in an Instant

On the left is an image preview of every page of this document, and below are the first 150 words with formatting removed:

Maths coursework Phi function Investigating the Phi function The phi function is defined for any positive integer(n), as the number of positive integers not greater than and co-prime (have no factor other than 1 in common) to n Example So (12) = 4 because the integers less than 12 which have no factors in common with it except for 1 are 1,5,7,11 i.e. there is 4 of them. I started to investigate the phi function of numbers from 2 to 24 so I could find patterns, which I can use to create a formula for the(n) term (n) Shared factors Not sharing factors (2) - 1 (2) = 1 (3) 1,2 (3) = 2 (4) 2 1,3 (4) = 2 (5) 1,2,3,4 (5) = 4 (6) 2,3,4 1,5 (6) = 2 (7) 1,2,3,4,5,6 (7) = 6 (8) 2,4,6 1,3,5,7 (8) = 4 (9) 3,6 1,2,4,5,7,8 (9) = 6 (10) 2,4,6,8,5 1,3,7,9 (10) = 4 (11) 1,2,3,4,5,6,7,8,9,10 (11) = 10 (12) 2,4,6,8,10,3,9 1,5,7,11 (12) = 4 (13) 1,2,3,4,5,6,7,8,9,10,11,12, (13) = 12 (14) 2,4,6,8,10,12,7 1,3,5,11,13 (14) = 6 (15) 3,5,9,12,6,10 1,2,4,7,8,11,13,14 (15) = 8 (16) 2,4,6,8,10,12,14 1,3,5,7,11,13,15 (16) = 8 (17) 1,2,3,4,5,6,7,8,9,10,11,12,13, 14,15,16 (17) = 16 (18) 2,3,4,6,8,10,12,14 1,5,7,11,13,17, (18) = 6 (19) 1,2,3,4,5,6,7,8,910,11,12,13,14, 15,16,17,18 (19) = 18 (20) 2,4,6,8,10,12,1,4,16,18,5,15 1,2,4,5,8,10,11,13,16,17,19 (20) = 8 (21) 3,6,9,12,15,18,7,14 1,2,4,5,8,10,11,13,16,17,19,20 (21) = 12 (22) 2,4,6,8,10,12,14,16,18,20,11 1,3,5,7,9,13,15,17,19,21 (22) = 10 (23) 3,6,12,8,15,18,21,16 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15 16,17,18,19,20,21 (23) = 22 (24) 2,4,6,8,10,12,14,16,18,20,22 6,3 1,5,7,11,13,17,19,23 (24) = 8 Part 1 i. (3) = 2 ii. (8)...

To see the full version of this document, and 145,348 others