& Numbers Polys
MAS3300
Prof. JLF King
4Jun2008
C1:
80pts
C4:
80pts
C5:
80pts
Total:
Notes exam. Please write solutions for C3,C4,C5 on
separate sheets of paper.
Write expressions unambiguously e.g, 1/a + b should be bracketed either [1/a] + b or
1/[a + b]. Be careful with negative signs!
40pts
C3:
Note. This is an open brain, open (pristine) Sigmon-
70pts
C2:
Exam-C
350pts
Every if must be matched by a then.
Short answer; show NO work.
a
C1:
Let := Gcd(165, 63) and nd particular
integers so that 165A + 63B = . Then
= , A= , B = .
Print
name
Ord:
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b
Note that Gcd(15, 21, 35) = 1. Find particular
integers S, T, U so that 15S + 21T + 35U = 1:
S= , T = , U = .
[Hint: Gcd Gcd(15, 21), 35 = 1.]
C2: Let
AT AF Nei mean Always
True, Always False, and Neither, respectively.
Let represent q a general non-zero rational number
and let x, y denote general irrationals. Please
circle
the best answer.
The product x y is irrational.
AT
AF
Nei
The sum x + y is irrational.
AT
AF
Nei
q x is irrational.
AT
AF
Nei
q + x is irrational.
AT
AF
Nei
Essay questions. Please write in complete
sentences.
C3: Prove that is
15
irrational.
Now prove that 3 + 5 is irrational.
C4: Consider two posints A and B . Prove directly,
using WO, that there is a posint D st.
DZ
=
AZ + B Z .
Honor Code: I have neither requested nor received
[Hint: Dont forget to rst show that AZ + B Z has a
non-zero element.]
C5: Prove that there are innitely many prime numbers.
End of Exam-C
help on this exam other than from my professor (or his
colleague).
Signature:
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