# Monthly Archives: April 2015

## Integer which is a palindrome in precisely 3 consecutive bases (excluding base 10)

## Find in base-6 a 9-digit square of the form AAAAAAXYZ

Hint :   it is the square of a number whose central triad is XYZ Answer:   333333521   base-6     David found:

## Num3er 952

is the sum of the cubes of its digits plus the product of its digits:     Can you find other examples?   Paul found:                         … Continue reading

Posted in Number Puzzles | Tagged , | 3 Comments

## Integers n such that n(n+1) = (n+2) (mod n+3)

Solve the following: (1)     (2)   where     is not necessarily     (3)

## When the product of two positive integers is even

Prove that the product of the positive integers a and b is even if and only if there exist positive integers c and d such that                                                                        … Continue reading

## Perfect squares formed by the last d-digits exceeding the first d-digits by 1

that is,         (Concatenation of 6099 and 6099+1)

## Inequality: 2^(b+c) + 2^(c+a) + 2^(a+b) < 2^(a+b+c+1) + 1

Prove that

## Equation: x^(a+b) + y = (x^a)(y^b)

Solve when   a,   b,   x,   y   are in