

Due date if any

Fuchsia means graded homework.



303 April/May


Section 8.2: 1, 2, 5, 6ac, 8.

Section 8.1: 9, 11.

For later problems, reading
Order of an Element may be helpful.



2327 April


Section 8.1: 1, 2, 3.

For the following problem, reading
Dirichlet Convolution (a slightly longer
version) may be helpful.
If r is multiplicative and invertible, then so is its Dirichlet inverse
r^{ 1}.

Section 7.4: 15, 16.



1620 April


Section 7.3: 1c, 4, 5, 7, 11c, 13.

Section 7.2: 1, 3, 4ab, 5, 8, 10, 20.

For the following problem, reading
Dirichlet Convolution (the short version)
may be helpful.
Generalize Theorem 6.4 of page 109 as follows.
If r and s are multiplicative, then so is their Dirichlet
convolution r * s.

Section 6.2: 1, 3, 4abc.



913 April


Section 6.1: 1, 6, 7, 8, 9, 12, 14, 22.



46 April


Section 5.3: 1, 6, 9, 10.

Section 5.2: 18.



26 March




1923 March


Section 5.2: 3, 4ad, 6a, 9.

Section 5.2: 1, 2ab.



59 March


Section 4.4: 1abcd, 2ac, 3, 6, 10.

Section 4.3: 19.

Section 4.2: 9, 16.



262 Feb/March


Section 4.3: 6ab, 9, 23.

Section 4.3: 2a, 4, 5a.

Section 4.2: 13, 15.

Section 4.2: 1, 3, 4, 8a.



1923 February


Section 3.2: 2, 3, 13 (hard problem, but good).

Find the prime factorizations of 123456789 and of 987654321.

Section 3.1: 9a.

Section 3.1: 3, 6.



1214 February


Section 2.5: 8a.

Section 2.5: 2, 5a, 6.



59 February


Section 2.5: 1.

Section 2.4: 5a, 8.

Section 2.4: 2cd, 4ab, 6.

Section 2.3: 19a, 20abc, 21.



292 Jan/February


Section 2.3: 4b, 12, 14, 18.

Section 2.3: 2, 6.

Section 2.2: 2, 4.

Section 2.1: 1, 2, 10.



2226 January


Convert the decimal number 99 into binary.
Convert the binary number 10101 into decimal.

When we expand (a+b)^13, what is the (binomial) coefficient in front of
a^9*b^4?
Write your final answer as a decimal number.

Section 1.2: 1, 8.

Think of a good more general formula than the one in Section 1.2.2.
Then try to prove this more general formula to be correct.

Consider the sequence a_1, a_2, a_3, a_4, a_5, ... defined by

a_n = 1/(1*2) + 1/(2*3) + 1/(3*4) + 1/(4*5) + ... + 1/(n*(n+1)).

By trial and experiment find a `closed' simple expression for a_n.

Prove by induction on n that this `closed' simple expression for a_n is always
correct.

Section 1.2: 2, 3.



1719 January


Section 1.1: 8.
Also, compute 12! (twelve factorial).
Also, consider the sequence a_1, a_2, a_3, a_4, a_5, ... defined by

a_1 = 1, and for all n >= 2 we have a_n = a_1 + a_2 + a_3 + ... + a_(n1).

By trial and experiment find a `closed' simple expression for a_n.

Prove by induction on n that this `closed' simple expression for a_n is always
correct.

Section 1.1: 1ae, 2, 9.
