0
answers
0
watching
223
views
10 Nov 2019
Define a function : Z Z such that ?(n) is the number of units in the ring Z/nZ. (a) If p is prime, then compute ?(p). (b) Compute t(6), ???'(10), and ???(15). Conjecture the value of t(pq) when p and q are prime and ptq. (e) A theoremof Eer states that if ged(a,n), the1 (mod n). Using this theorem and part (a), prove that every element of Z/pZ is a root of the polynonial ??-? ?n?/Pz1x]. In other words, prove that for any integer a the congruence a a (mod p) holds
Define a function : Z Z such that ?(n) is the number of units in the ring Z/nZ. (a) If p is prime, then compute ?(p). (b) Compute t(6), ???'(10), and ???(15). Conjecture the value of t(pq) when p and q are prime and ptq. (e) A theoremof Eer states that if ged(a,n), the1 (mod n). Using this theorem and part (a), prove that every element of Z/pZ is a root of the polynonial ??-? ?n?/Pz1x]. In other words, prove that for any integer a the congruence a a (mod p) holds
0
answers
0
watching
223
views
For unlimited access to Homework Help, a Homework+ subscription is required.