Smith Numbers While skimming his phone directory in 1982, mathematician Albert Wilansky noticed that the telephone number of his brother-in-law H. Smith had the following peculiar property: The sum of the digits of that number was equal to the sum of the digit…

From Euclid, it is known that for any positive integers A and B there exist such integers X and Y that AX + BY = D, where D is the greatest common divisor of A and B. The problem is to find the corresponding X, Y, and D for a given A and B.

There is man named Mabu who switches on-off the lights along a corridor at our university. Every bulb has its own toggle switch that changes the state of the light. If the light is off, pressing the switch turns it on. Pressing it again will turn it off. Initi…

<p>Certain cryptographic algorithms make use of big prime numbers. However, checking whether a big number is prime is not so easy. Randomized primality tests exist that offer a high degree of confidence of accurate determination at low cost, such as the …

Self-describing Sequence Solomon Golomb's self-describing sequence {f (1), f (2), f (3),...} is the only non-decreasing sequence of positive integers with the property that it contains exactly f (k) occurrences of k for each k. A few moment's thought reveals t…

Consider the process of stepping from integer x to integer y along integer points of the straight line. The length of each step must be non-negative and can be one bigger than, equal to, or one smaller than the length of the previous step. What is the minimum …