Some solutions - UWO Math. Dept. home page
... than fives, so in fact it suffices to count the fives. That is, we need to count how many fives occur as factors of 1, 2, · · · , n. We have to be careful since some numbers, such as 25, have more than one five. To begin with, we count those numbers that have at least one factor of 5; that is, we co ...
... than fives, so in fact it suffices to count the fives. That is, we need to count how many fives occur as factors of 1, 2, · · · , n. We have to be careful since some numbers, such as 25, have more than one five. To begin with, we count those numbers that have at least one factor of 5; that is, we co ...
Full text
... we get an almost arithmetic sequence, by Lemma 3. Suppose now b <_ -1. Then the integers m satisfying (-mr + s) <_ (~br) form an almost arithmetic sequence. Thus, by Lemma 1,those integers m satisfying (-mr + s) > (-br) = 1 - (br), or equivalently, (mr - s) = 1 - (-mr + s) < (br), form an almost ari ...
... we get an almost arithmetic sequence, by Lemma 3. Suppose now b <_ -1. Then the integers m satisfying (-mr + s) <_ (~br) form an almost arithmetic sequence. Thus, by Lemma 1,those integers m satisfying (-mr + s) > (-br) = 1 - (br), or equivalently, (mr - s) = 1 - (-mr + s) < (br), form an almost ari ...
UNIVERSITY OF CALICUT SCHOOL OF DISTANCE EDUCATION CORE COURSE B.Sc. MATHEMATICS
... 71. The set S is open then which of the following is true (a) S does not contain if boundary points (b) S contains its boundary points (c) S have its boundary points (d) None of these 72. A metrix Space X satisfies Bolzano wierstrass property then (a) Every infinite sequence ( ...
... 71. The set S is open then which of the following is true (a) S does not contain if boundary points (b) S contains its boundary points (c) S have its boundary points (d) None of these 72. A metrix Space X satisfies Bolzano wierstrass property then (a) Every infinite sequence ( ...
