Tagged Questions
5
votes
4answers
83 views
Prove or disprove the following statements involving greatest common divisor
Help with prove or disproving either of these statements would be really appreciated, one or the other is fine, I just need a start or a solution to one and I'm sure I could probably figure the other ...
-1
votes
1answer
59 views
Proof of divisibility by 2 and 3 if and only if divisible by 6
I can't find a way of proving that:
For integer a, a is divisible by 2 and divisible by 3 if and only if a is divisible by 6.
I’m not sure where to go from here. Any help would be great!
1
vote
1answer
30 views
Pointers about the concept of 'division extensionality'?
When working a bit on another question (If $a \equiv b\pmod m$, then $\gcd(a, m) = \gcd(b, m)$), I discovered the following, which seems to be valid:
$$
a = b \;\;\equiv\;\; \langle \forall d :: d ...
0
votes
2answers
80 views
Decimal Representaion
A rational number can be represented in the form p/q. prove that the period of the the repeating decimal should at the most q-1.
1
vote
1answer
63 views
Proving that if $xo + yp = 1$, then $\gcd(o,p) = 1\;$?
I'm currently trying to prove the equation that you see above.
I know that it must have something to do with the laws of divisibility, and these rules in conjunction with rules about integers, but ...
1
vote
2answers
138 views
Help understanding divisibility proofs
Can someone please explain how to do this problem?
Prove or disprove the statement “If $a \mid b$ and $c \mid d$, then $(a + c)\mid(b + d)$”.
1
vote
2answers
130 views
Prove that $2^n | P(2n, n)$
I am attempting to use Induction to prove this, but I am not sure if it is the right method to take. Here is what I have tried:
Induction Hypothesis:
Assume $P(k)$ is true for some fixed $ k \geq 1$ ...
4
votes
2answers
291 views
Proving divisibility
Let $x,y$ and $m$ be integers. Prove if $m | 4x$ + y and $m | 7x+2y$ then $m|x$ and $m|y$
