# Monthly Archives: June 2015

## Cyclic permutation of digits – GeometricMean[abc, bca] = cab

Can you find other solutions?

## Concatenation – Emirps

An emirp is a prime number that results in a different prime when its digits are reversed. https://en.wikipedia.org/wiki/Emirp Let’s take all the emirps < 1000 13, 17, 31, 37, 71, 73, 79, 97, 107, 113, 149, 157, 167, 179, … Continue reading

## Sequences of squares: a+1, ab+1, abc+1, abcd+1, …

There exist an infinite number of infinite sequences of distinct positive integers    , … for which     , … are all squares.     then,     then,     then,     then,   etc.   … Continue reading

## Triangular numbers which are the sum of 7 consecutive squares

The first few solutions:

## Solutions to: Sum of 47 consecutive Squares is Square

Posted in Number Puzzles | Tagged | 2 Comments

## When Concatenations 13||N^2|| and 17||N^2||71 are prime

Find     such that the concatenation (1)     is a prime number (2)     is a prime number     For all                           … Continue reading

Posted in Prime Numbers | Tagged | 1 Comment

## Triangular numbers that are sum of 11 consecutive squares

## Solutions to: Sum of 33 consecutive Squares is Square

Posted in Number Puzzles | Tagged | 3 Comments

## Concatenation 11 || N^3 || 11 is a prime number (Part 2)

Find     such that the concatenation     is a prime number For all