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Archimedes' axiom, also known as the continuity axiom or Archimedes' lemma, survives in the writings of Eudoxus (Boyer and Merzbach 1991), but the term was first coined by ...

Select three points at random on the circumference of a unit circle and find the distribution of areas of the resulting triangles determined by these three points. The first ...

A discrete function A(n,k) is called closed form (or sometimes "hypergeometric") in two variables if the ratios A(n+1,k)/A(n,k) and A(n,k+1)/A(n,k) are both rational ...

delta(x-t)=sum_(n=0)^inftyphi_n(x)phi_n(t), where delta(x) is the delta function.

A complete set of mutually conjugate group elements. Each element in a group belongs to exactly one class, and the identity element (I=1) is always in its own class. The ...

The cuban primes, named after differences between successive cubic numbers, have the form n^3-(n-1)^3. The first few are 7, 19, 37, 61, 127, 271, ... (OEIS A002407), which ...

Form a sequence from an alphabet of letters [1,n] such that there are no consecutive letters and no alternating subsequences of length greater than d. Then the sequence is a ...

The Diffie-Hellman protocol is a method for two computer users to generate a shared private key with which they can then exchange information across an insecure channel. Let ...

The 2-1 equation A^n+B^n=C^n (1) is a special case of Fermat's last theorem and so has no solutions for n>=3. Lander et al. (1967) give a table showing the smallest n for ...

Euler (1772ab) conjectured that there are no positive integer solutions to the quartic Diophantine equation A^4=B^4+C^4+D^4. This conjecture was disproved by Elkies (1988), ...