Number theory: homework

Here are the homework assignments. Orange ones are for the grader, and purple ones are for me.

Worksheets and daily handouts
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Number 1: due Monday 13 January
Read Chapter 0 and do at least 5 "different" problems from the end of the chapter.

Number 2: due Wednesday 15 January
Section 1.1: 13,15,16,20,22,25,28,29

    Number 3: due Friday 17 January
            Section 1.2:    3,8,10,13,15,18,19,22,29,31
            Section 1.3:    2,5,9,12,14,17,19

    Number 4: due Wednesday 22 January
            Section 1.4:    2,10,15,20,22,32,39    (also do 1,7,13,23,28, but don't turn them in)
            Section 1.5:    29,31,33,37,39,40,47    (also do 1-16, 27,38 but don't turn them in)

    Number 5: due Friday 24 January
            Section 1.3:    23,24,25
            And:    prove that the divisibility test for 9 works.
    Revisions are due Wednesday 5 February.

    Number 6: due Monday 27 January
            Read Section 4.1
            Section 4.1:    25,26,35,40

Number 7: due Wednesday 29 January
Section 4.1: 1,2,27,28,39,42,43,44

Number 8: due Friday 31 January
Section 4.2: 1,2,5,23,24,42

OUR FIRST TEST IS MONDAY 3 FEBRUARY

    Number 9: due Friday 7 February
            Section 2.1:    11,12,17,39
            Section 2.2:    5,6,9,10,13,14,15
            Also work on problem 3 from today's worksheet, but don't turn it in.

    Number 10: due Monday 10 February
            Read Sections 2.4 and 2.5
            Section 2.3:    7,35
            Section 2.4:    1,2,11,12,34
            Section 2.5:    8,16,19

Number 11: due Wednesday 12 February
Do the back of Monday's worksheet.

    Number 12: due Friday 14 February [NOTE: now due Monday 17 Feb]
            Section 2.3:    21,23,25,27,29;
            Prove: if a>0 and n>1 are integers and aⁿ-1 is prime, then a=2 AND n is prime.
            Prove: if a>0 and n>1 are integers and aⁿ+1 is prime, then a=1 OR n is a power of 2.
            (These last two problems are almost identical to Section 3.4, problems 17 and 19.)

Number 13: due Friday 21 February
These three problems

    Number 14: due Wednesday 26 February
            Section 3.2:    7,8,12,14,15,16
            Read Section 3.6

    Number 15: due Friday 28 February
            Section 3.2:    17,18,19
            Section 3.6:    5,9,11,17

    Number 16: due Monday 3 March
            Section 3.2:    25
            Section 3.5:    53
            Plus: Let     lambda(n) = (-1)^e1+e2+...+ek    where n=p₁^e1p₂^e2...p_k^ek.
                Find a formula for     (U * lambda)(n),     i.e. the sum over all divisors d of n of lambda(d).

Number 17: due Wednesday 5 March
Section 4.3: 12,14,32,47,48

Number 18: due Friday 7 March
These problems

OUR SECOND TEST IS FRIDAY 14 MARCH

Number 19: due Wednesday 26 March
Section 5.1: 2,4,16,18,27,29

Number 20: due Friday 28 March
Section 5.2: 5,9,12,18

    Number 21: due Monday 31 March
            Section 5.3:    40,41,43
            Section 5.4:    1,2,3,4,35

    Number 22: due Friday 4 April
            Section 5.4:    45,46,47
    This one is optional: it'll be extra credit if 4 or fewer people do it, and regular homework if 5 or more do it.

Number 23: due Monday 7 April
These problems

OUR THIRD TEST IS FRIDAY 11 APRIL

Number 24: due Friday 18 April
Section 6.5: 17,18,19,20,21

Number 25: due Wednesday 23 April
Section 7.1: 6,10,20,32,33,34

Number 26: due Friday 25 April
Section 7.2: 15,16,19,20

Number 27: due Monday 28 April
These problems

Number 28: due Wednesday 30 April
Section 7.2: 21,22

OUR FINAL EXAM IS MONDAY 5 MAY, FROM 7-10 PM, IN ROOM 304 BOYD