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Arnauld's paradox states that if negative numbers exist, then (-1)/1 must equal 1/(-1), which asserts that the ratio of a smaller to a larger quantity equals the ratio of the ...

If bc=bd (mod a) and (b,a)=1 (i.e., a and b are relatively prime), then c=d (mod a).

A canonical brick is a 1×2×4 cuboid.

Construct a 5×5×5 cube from thirteen 1×2×4 blocks, one 2×2×2 block, one 1×2×2, and three 1×1×3 blocks.

A set S of positive integers is said to be Diophantine iff there exists a polynomial Q with integral coefficients in m>=1 indeterminates such that ...

A partial order defined by (i-1, i), (i+1, i) for odd i.

A set S is said to be GCD-closed if GCD(x_i,x_j) in S for 1<=i,j<=n.

Let A be a unital C^*-algebra, then an element u in A is called an isometry if u^*u=1.

The recurrence relation (n-1)A_(n+1)=(n^2-1)A_n+(n+1)A_(n-1)+4(-1)^n valid for n=4, 5, ... with A(2)=0 and A(3)=1 and which solves the married couples problem (Dörrie 1965, ...

The ordinary differential equation y^'=-y(1+kappa(x)y)/(1-kappa(x)y).