North Carolina State University is a landgrant university and a constituent institution
of The University of North Carolina
Department of Mathematics
NC STATE UNIVERSITY
MA 410 Theory of Numbers, nal examination, May 6, 2011
Prof. Erich Kaltofen <kaltofen
North Carolina State University is a landgrant university and a constituent institution
of The University of North Carolina
Department of Mathematics
NC STATE UNIVERSITY
MA 410 Theory of Numbers, nal examination, May 5, 2010
Prof. Erich Kaltofen <kaltofen
North Carolina State University is a landgrant university and a constituent institution
of The University of North Carolina
Department of Mathematics
NC STATE UNIVERSITY
MA 410 Theory of Numbers, nal examination, May 7, 2012
Prof. Erich Kaltofen <kaltofen
North Carolina State University is a landgrant university and a constituent institution
of The University of North Carolina
Department of Mathematics
NC STATE UNIVERSITY
MA 410 Theory of Numbers, nal examination, May 4, 2005
[email protected] (email)
Problem
(a,

(16 points)
4pts) Please compute 21ffi mod 10. Please show your work.
2too=O
[,^d z)
2'* = e),'
=i
(b, 4pts) True of false: For all integers r
your answer.
Tv,*.
(c,4pts)
I*t p:ll
to form
7+1
<:
l+t
(d,4pts)
and
Q,"A 5
,!,2 e Z>o with *
C"l
Problem 1 (16 Points)
remaindering and Euler's generalization
(a, 4pts) please compute 21000000 mod 55. Hint: use Chinese
of the little Fermat theorem.
?'
loc)c>o0o
L
"'\
+pglt*"
(O,
rooo ao
,rt^*d.f .2
L,td t\ Y?
o
*d +
: ?o= \
'^Jro :zo =t
Please expl
Problem 1 (16 points)
(a,4pts) Please cornpute 21m mod 100. Please show your work.
l0o=*
2r0oh"*J,
z2:e
GJ.r), cfw_trrl = 25 (' i)
*76=o'l*A g = r'+= Zo
t
,'"'=V")'=\
zv+a rbtt
Ttoo
d
o
lo0 = lG
lr"J to tu rl
(b,4pts) Trueorfalse: If pisaprimenumbertheno