Determine if a rational number is also an integer, without any form of dividing. The input should be any pair of numerator and denominator. Don't forget to consider negative numbers, and division by zero. Dividing is defined as any operation/function that gives a quotient or reminder, even if it ...

Consider a triangle \$ABC\$ whose sides \$BC,CA,AB\$ have lengths \$a,b,c\$ respectively. In this triangle we can construct circles \$G_A,G_B,G_C\$ such that \$G_A\$ is tangent to \$CA,AB,G_B,G_C\$ \$G_B\$ is tangent to \$AB,BC,G_C,G_A\$ \$G_C\$ is tangent to \$BC,CA,G_A,G_B\$ These are the Ma...

Given an alphabet's cardinality, \$n>0\$, and an occurrence limit, \$k>0\$, produce the number, \$a(n, k)\$, of strings that may be constructed from the \$n\$ letters in the alphabet which have no more than \$k\$ occurrences of any letter. Count the empty string, or don't, it's up to you. This is...