# Tagged Questions

89 views

A few nights ago I couldn't sleep and so started doing this: I would take a number and add up all of its digits to get a new number and then add up all of those digits and so on until there was only ...
68 views

### Unexplanied pattern from increasing rational sequences

I've stummbled upon some strange pattern when working with series of rational numbers. If anyone could shed light on this phenomenon I will be most greatful. Backgroud: Working in an integer lattice ...
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### Number of differently-sized squares needed to fill a rectangle; is there a visible formula? [Pattern spotting]

Consider a game in which we tile a given rectangle with the largest squares that will fit. We record the number of squares of each size that we can use, until the rectangle is completely covered. ...
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### Largest number on multiplying with itself gives the same number as last digits of the product

What is the largest number on multiplying with itself gives the same number as last digits of the product? i.e., $(376 \times 376) = 141376$ i.e., $(25\times 25) = 625$ If the largest number cant ...
71 views

### finding all pairs $(x,z)$

How to find all pairs $(x,z)$ of integers for which $2(z+1)^3$ is divisible by $xz-1$