# Tag Archives: Concatenation

## Concatenation : a || b = n^2 + a = (n+1)^2 – b

Notice that The integer N = 122 can be partitioned into two parts, 1 and 22, so that the first part is the difference between N and the greatest square less than N, and the second part is … Continue reading

## Concatenation: aa||bb||cc||dd + 1, aaa||bbb + 1 are squares

Numbers of the form     such that     is a square :     …………………….. …………………….. …………………………. …………………………. ………………………. ……………………….   Numbers of the form     is a square : ……………………………. …………………………….     ………………………………… … Continue reading

## Concatenations : x || y || z = (x + y + z)^3

For example,     Can you find other solutions?

## Concatenation | 7-digit number abc = a || b || c

a,   b,   c   are in arithmetic progression a   ||   b   ||   c   =   abc   is a 7-digit number Find the largest 7-digit number obtained in this way.   … Continue reading

Posted in Number Puzzles | Tagged | 5 Comments

## Concatenations : x || y = x^2/2 + 2*y^2

where     and     are positive integers

## Concatenation: 2^n || 2^(n+1)

Let     be any positive integer.   Prove that     is always a multiple of 3.

## Concatenations: x^2 || 2^2 = y^2

## Concatenations x^2 || 3^2 = y^2

Here are the first few solutions to

## Concatenations Oblong numbers| O(n) || x^2 = A^2

An Oblong number is a number of the form     Here are the first few solutions for                                           … Continue reading

## When the Concatenation of n || (n+1) is Octagonal

Octagonal numbers are of the form      We can write Or the integer length of     is     Here are the first few solutions   n   =   1,   2,   5,   … Continue reading