# Monthly Archives: March 2016

## Integers w/ 4 different partitions into 3 parts w/ the same product

Partition (number theory) https://en.wikipedia.org/wiki/Partition_(number_theory)     Find integers     that have 4 different partitions into 3 parts with the same product and with the same product,                        … Continue reading

Posted in Number Puzzles | Tagged | 4 Comments

## fractional part of (6*sqrt(6) + 14)

Prove that if    ,   then

## The square of a Fibonacci number

Show that is the square of a Fibonacci number

## Fibonacci numbers | is 5 F^2_{2k} + 4 always a square number?

Is     always a square number? Also, is     always a square number?

## Fibonacci numbers | F(n) < x < F(n+1) < y < F(n+2)

If   then show that     is never a Fibonacci number

## Fibonacci numbers – Identity

Establish the identity:

## Alphametric puzzles — Part 1

Definition:   An alphametic puzzle is an arithmetic problem involving words where there is a one-to-one mapping between letters and digits that makes the arithmetic equation true.   (1) in base 8,     is a prime number Solved … Continue reading

Posted in Number Puzzles | Tagged | 2 Comments

## Heron triangles & half-angle formulae

Prove that If the sides of a triangle are in arithmetic progression if and only if the cotangents of its half-angles ,    ,    are also in arithmetic progression   Also,   if and only if       … Continue reading