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The Smarandache function mu(n) is the function first considered by Lucas (1883), Neuberg (1887), and Kempner (1918) and subsequently rediscovered by Smarandache (1980) that ...

An amicable quadruple as a quadruple (a,b,c,d) such that sigma(a)=sigma(b)=sigma(c)=sigma(d)=a+b+c+d, (1) where sigma(n) is the divisor function. If (a,b) and (x,y) are ...

A Brier number is a number that is both a Riesel number and a Sierpiński number of the second kind, i.e., a number n such that for all k>=1, the numbers n·2^k+1 and n·2^k-1 ...

C_5 is the unique group of group order 5, which is Abelian. Examples include the point group C_5 and the integers mod 5 under addition (Z_5). No modulo multiplication group ...

C_7 is the cyclic group that is the unique group of group order 7. Examples include the point group C_7 and the integers modulo 7 under addition (Z_7). No modulo ...

Let G be a group of group order h and D be a set of k elements of G. If the set of differences d_i-d_j contains every nonzero element of G exactly lambda times, then D is a ...

To divide is to perform the operation of division, i.e., to see how many times a divisor d goes into another number n. n divided by d is written n/d or n÷d. The result need ...

The central binomial coefficient (2n; n) is never squarefree for n>4. This was proved true for all sufficiently large n by Sárkőzy's theorem. Goetgheluck (1988) proved the ...

Fischer's z-distribution is the general distribution defined by g(z)=(2n_1^(n_1/2)n_2^(n_2/2))/(B((n_1)/2,(n_2)/2))(e^(n_1z))/((n_1e^(2z)+n_2)^((n_1+n_2)/2)) (1) (Kenney and ...

A problem listed in a fall issue of Gazeta Matematică in the mid-1970s posed the question if x_1>0 and x_(n+1)=(1+1/(x_n))^n (1) for n=1, 2, ..., then are there any values ...