Issuers tack it on so that the whole card number will satisfy a specific mathematical test—the Luhn algorithm. Here’s how the algorithm works: Write out all but the last digit of the card number.

Osborne (1975) introduces a modified Prony algorithm for fitting sum of exponential to the real data sets. Smyth (1985) and Osborne and Smyth (1990) investigate the stability of the algorithm. They ...

Mathematicians long wondered whether it’s possible to express the number 33 as the sum of three cubes — that is, whether the equation 33 = x ³+ y ³+ z ³ has a solution. They knew that 29 could be ...