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The base-60 notational system for representing real numbers. A base-60 number system was used by the Babylonians and is preserved in the modern measurement of time (hours, ...

A conjecture that, as proved by Parshin (1968), implies the Mordell conjecture.

A Shanks (a,b)-chain is a sequence of primes p_i of the form p_(i+1)=ap_i^2-b, with a and b integers. On Sep. 1, 2000, P. Leyland found a (4, 17)-chain of length 6, and on ...

Let f_1(z), ..., f_m(z) for m>=1 be a set of E-functions that (1) form a solution of the system of differential equations y_k^'=q_(k0)+sum_(j=1)^mq_(kj)y_j for q_(kj) in C(z) ...

The transformation T(x) = frac(1/x) (1) = 1/x-|_1/x_|, (2) where frac(x) is the fractional part of x and |_x_| is the floor function, that takes a continued fraction ...

A knot used to shorten a long rope.

If a fixed fraction x of a given amount of money P is lost, and then the same fraction x of the remaining amount is gained, the result is less than the original and equal to ...

sum_(n=1)^(infty)1/(phi(n)sigma_1(n)) = product_(p prime)(1+sum_(k=1)^(infty)1/(p^(2k)-p^(k-1))) (1) = 1.786576459... (2) (OEIS A093827), where phi(n) is the totient function ...

A nonzero ring S whose only (two-sided) ideals are S itself and zero. Every commutative simple ring is a field. Every simple ring is a prime ring.

A set having exactly one element a. A singleton set is denoted by {a} and is the simplest example of a nonempty set.