# Tagged Questions

811 views

### Find the least value of x which when divided by 3 leaves remainder 1, …

A number when divided by 3 gives a remainder of 1; when divided by 4, gives a remainder of 2; when divided by 5, gives a remainder of 3; and when divided by 6, gives a remainder of 4. Find the ...
125 views

### $2^5 \cdot a^b=2,5ab$

I came across this problem in an elementary number theory book, and I think I solved it. Well, the question is posed as $2^5 \cdot 9^2 = 2,592$. Are there any other pairs $a,b \in \mathbb{Z}$ such ...
478 views

### Is $\sum_{k=1}^{n} k^k / \sum_{k=1}^{n} k \in \mathbb{N}$ for some $n > 1$?

Let $A = \sum_{k=1}^{n} k^k$ and $B = \sum_{k=1}^{n} k$, where $n >1$ is a positive integer. Is $A/B$ ever an integer?
1k views

### How does the divisibility graphs work?

I came across this graphic method for checking divisibility by $7$. $\hskip1.5in$ Write down a number $n$. Start at the small white node at the bottom of the graph. For each digit $d$ in ...
495 views

### Divide by a number without dividing.

Can anyone come up with a way to divide any given x by any given y without actually dividing? For example to add any given x to any given y without adding you would just do: $x-(-y)$ And to ...