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1. if a doesn't divide b and a doesn't divide c , then a doesn't divide b times c.
give a counterexample to show this is a false statement.
2. if a divides c and b divides c sometimes, a times b divides c and sometimes it doesn't
show an example when a times b divides c .
show and example when a times b doesn't divide c.
a can't be divided byQuote:
Originally Posted by lonestarross
, and a can't be divided by
, but a can be divided by
Note that
I'm not 100% positive with my answer though:D
You know of a numerical example of this?
Usually with this language and nothing else specified, we assume we are working over the integers.Quote:
Originally Posted by lonestarross
(1) is very simple.. don't know how to give a hint, here's such a counterexample, learn from it
a = 2*3
b = 2*5
c = 3*5
(2) this is confusing. Is the first part supposed to mean
if (a divides c) and (b divides c sometimes)
or
if (a divides c and b divides c) sometimes
?
I'll assume the first. But it can be proven with the stricter requirement "a divides c and b divides c always".
Just use simple examples. For the case ab divides c, let c = ab. For ab does not divide c, let a = b = c > 1.
the first.\\ but when you say a=2*3, b=2*5, c=3*5, 5 does divide 10 and 15...never mind i t is backwards
Okay, my response addresses this.Quote:
Originally Posted by lonestarross
so for 2. ab|c a=2 b=3 c=6 2*3|6
ab doesn't |c 4*6|12
still dont get (1) 2*3- 5 2*5- 10 2*3- 15 a will |b 5\10
on
thank you for your help. got it and understand it now