We say a number is ascending if it's digits are strictly increasing. For example, 189 and 3468 are ascending while 142 and 466 are not. For which ascending number n is 6n also ascending?
I have got the answer to this problem after a while with some guess and check, but I would like to know a...
i have this in my lecture notes "
An ascending filter F is non-bounded subset of algebra A in which any two elements are both exceeded (in the sense of >=) by some elements of F.
the supremum of F is the smallest element in A with a=<sup F for all a belongs to the F . "
when it says...
How many four digit numbers can be formed from the digits from 1 to 9 inclusive, if repetitions are not allowed?
i. How many of these are divisible by 5?
ii. How many are divisible by 2?
iii. How many of these contain digits in ascending order eg 1459?
I've done i and ii and i got 336 and 1344...
Let R be a UFD, a in R*\U(R), a =p_1^(a_1).......p_t^(a_t) for distinct non-associated primes p_j, (a_j) >= 1, 1=<j=<t.
If d|a the show that d~p_1^(b_1).....p_t^(b_t) for some 0=<b_j=<a_j, 1=<j=<t.
Show that there are (1+a_1)....(1+a_t) distinct ideals (d) such that (a)=< (d). Deduce that...