MATH 135 Algebra, Assignment 7
Due: Wed Nov 4, 8:30 am
1:
(a) Find the smallest nonnegative integer
x
such that
x
≡
41 (mod 9).
(b) Find the integer
x
which has the smallest absolute value such that
x
≡
568 (mod 41).
(c) What day of the week will it be 1000 days after a Monday?
(d) What time of day will it be 1000 hours after 5:00 pm?
(e) Exactly what time of day will it be 1 million seconds after 5:00 pm?
2:
(a) Find all positive integers
m
such that 126
≡
35 (mod
m
).
(b) Find the remainder when the integer
100
X
k
=1
k
! is divided by 13.
(c) Find the remainder when the integer
40!
2
20
·
20!
is divided by 8.
3:
Most recent books are identiﬁed by their
International Standard Book Number
, or ISBN,
which is a 10digit number, separated into four blocks. The ISBN for our course text book
is 0131848682. Here the ﬁrst block of digits, 0, represents the language of the book
(English), the second block, 13, represents the publisher (Pearson Prentice Hall), the third
block, 184868, is the number assigned to the book by the publisher, and the last block,
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 Spring '08
 ANDREWCHILDS
 Algebra, Remainder, ISBN, Natural number, Prime number, International Standard Book Number

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